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It's an extremely rare species of centipede, the Beige Frontrunner.

When you look at the part that resemble human pelvis, you notice something entirely unprecedented across the entire kingdom of Animalia -- a hole! Animals don't just make holes. They're hard to make, they don't provide any benefit, and they become a liability when the creature overlooks a tree branch at just the wrong height while they're running away. Closer inspection reveals the truth. It's a pair of chelicerae! Knowing this, we can finally figure out how the entire creature's body plan.

So... since the pelvis is actually a pair of chelicerae, then what looks like the coccyx must be the creature's head. What looks like the head must actually be the tail, and the rest must be limbs! The back pair and the front pair are extremely enlarged, while the rest are shorter and serve purely as mimicry. Some of them close at the front to make the appearance of a rib cage, while some are much shorter without much mobility.

Heck why, I hear you ask?
In the long past, the creature had two pairs of enlarged limbs that served primarily as defense. The creature's unusual posture - bipedal using the front pair of limbs - has evolved from how the creature used to escape from predators. You know, 20 pairs of limbs are hard to coordinate while you're trying to hit your top speed, and lifting on your hind legs requires them to temporarily move faster than your center of mass and then slow down. The Frontrunner's ancestors would instead just push against the ground and become upright in the other way, sacrificing the temporary boost of vantage point for a quicker departure from the impending doom.

The hind pair of limbs grew longer and stronger to make the transition to upright even faster, while the front pair grew longer and stronger to provide speed during the upright phase. Eventually the creature learned a new purpose for the hind legs - as manipulators, to grab fruit from bushes and trees. This, along metabolical benefits, pushed the creature to grow longer and thinner. In the mean time, the rest of its legs just ... stayed the same. some grew slightly longer to serve as secondary manipulators - function now lost - while some shrunk to just decorative stubs. The creature did have to grow thinner as it grew taller because otherwise it wouldn't be able to support its own weight!

Then come humans. A couple thousand years ago, one group of monkeys endemic to the Red Sea region has decided it would be a smart idea to start collecting their dead to one place to reduce the risk of being detected by predators - and Beige Frontrunners have quickly discovered a new survival strategy. Because they already resembled the skeletons of those monkeys, the Frontrunners that chose those boneyards as their resting spots found themselves mostly ignored by their usual predators. When the predators began to figure things out, Frontrunners had to improve their mimicry. It was not too long before those ridiculous bulges on their tails began to evolve, as well as the coloration and unusual head structure. The eyes finished their migration to the back of their heads. Their main limbs' tarsal claws grew longer for mimicry, and they even developed local coloration that resembles the fingers of a human hand, and a stripe that mimics the gap between the radius and ulna...

As to why Frontrunners cease to function when their tail decoration that resembles the human skull gets removed ... I would also lose my mind if somebody decided to just chop off my reproductory organs!

Your question boils down to "can you convert an endoskeleton to an exoskeleton?" Tto which the answer is basically "no", because each has evolved to fit its specific task and the nature of the joints in each is quite specialised.

For want of a better example, take a look at this. Its a japanese spider crab, which I think can grow to be one of the largest exoskeletonised animals in the world.

See how all the joints are enclosed? That's because all of the bits of the limbs where the muscles attach must be inside for the whole range of the joint's motion. What you can't see here is how the limbs have very thin strong walls to allow sufficient space inside for muscles. In both these cases, the limbs are the polar opposite of endoskeletal limbs.

Look how long and thin those limbs are. The muscle inside is quite slender, because the crab's body is lightweight and, crucially, supported by the water around it. Absent that support, it simply woulnd't be strong enough to support its own weight. If you wanted to make it as strong as a human (because who wants weakling skeleton monsters?) it would need to have limbs as thick as human limbs in order to fit in the huge slabs of muscle we have. Crustacean muscles aren't magically stronger and better than mammalian ones!

You'd need to do some considerable re-engineering, and the end result would still basically be a slightly rubbish compromise. If you had the technology (or magic) to turn a human skeleton into an exoskeleton, you'd still be better off making something more like a zombie (or mummy) or a giant crab instead. They're both still pretty terrifying, and they're mechanically much more sound so they could be tougher, stronger and faster.

Your theoretical hermit-crab-like thing that burrows into the joints of a corpse is no better off... it just wouldn't be able to exert enough force on those inappropriate joints to be strong, or fast, or tough. You could smash it apart with a big stick, I bet. It would also have to have quite a complex proprioceptive system to keep a human body upright and walking, which is a very complex operation. Oh, and there are a lot of joints; presumably it is some kind of cooperative, communal organism too. Humans have nerves to communicate with distant parts of their bodies, how would a horde of snails do it? Not very fast, I suspect.

So maybe if you wanted a fragile creature that could crawl along the floor very slowly at you, and that you could kick the head off with no effort, then you've got the right idea.

To some degree, this is a question of what you mean by "skeleton".

Exoskeletons are well established, though really large exoskeletal creatures on land might have issues with lack of support during molting -- you might have to have them grow their exoskeletons in a different way. However, the existing way arthropods work allowed sizes up to Arthropleura (up to 2.3 m/7.5 ft long and 50 cm/20 in wide) in Carboniferous conditions. (Of course, oxygen levels were higher then, but you could just give these creatures lungs -- exoskeletons don't require tracheal breathing; spiders have book lungs, and the coconut crab, the largest land arthropod, uses a bronchiostegal lung.)

Muscles inside something like a marrow cavity probably wouldn't have enough mass, unless it was just a thin outer bone layer outside a large cavity, which more or less comes back around to an exoskeleton.

If you want a creature that looks more like a vertebrate skeleton (bones with gaps between them, not a completely plated exterior), you could have a creature with largely transparent flesh and external bony armor over only certain areas of the body (eg vital organs). At first glance, with the organs largely hidden by bone and mostly-transparent gaps between, this could look very much like a "walking skeleton".

EDIT: From clarification in the comments that the intent is to "re-animate" the existing skeleton of another creature, the only one of these options that would work is the last one. A creature with mostly-transparent flesh and no hard parts of its own (something jellyfish-like) could take over the skeleton of another creature for structural support and/or protection of its soft flesh, the way a hermit crab uses another animal's shell for protection. (This is similar to how the Mistwraiths in Brandon Sanderson's Mistborn series function.)

"Normal" (<- quotes required in questions like this) humanoid with bioluminescent skeleton and tissues transparent to the specific frequencies it produces. Works as long as any other light source is weak enough that only the bones are really visible. On a downside sunlight would probably cause death by cancer after five seconds of exposure so underground and nocturnal only.

Realistically to see it would need to use the same frequencies it produces so the pupils would be visible. Probably it would have a reflector similar to one cats have so the pupils would actually glow fairly brightly.

Giving ability to control the glow in the bones might be a good idea. If only some of the skeletons give off bright light, the others would be very hard to spot but would be able to see using light from the lit ones. Modulation of the light can also be used to communicate silently.

The problem here is that the muscles, or whatever else is enabling the monster to move, would have to essentially be hidden inside the joints. This would give them very little leverage to move the limbs. Just think about your bicep. It wouldn't fit inside your humerus (your upper arm bone), and its attachment is a little bit up the forearm from the elbow joint to give it some leverage.

So basically you need muscle-equivalents that are very strong, since they won't have much leverage, and very narrow, to fit inside the bones. (Or maybe just super-compact, so they fit inside the joint area like little motors.) And the bones themselves would have to be super-strong since the forces of the super-muscles would be greater.

This is a very tall order. Perhaps there could be stringy muscle-tendon things with the strength of piano wire that came out of holes in the bone and attach about where our muscles actually do. Then you could see them, and maybe even lose a finger if the monster caught it between the muscle and a skeleton. You would still have to worry about the bones being strong enough to make this work, since the attachment points are really tiny.

Remember that you also need contact surfaces for the joints. These joints will work poorly with no cartilage.

The point is that, with enough ingenuity, you can come with a non-magical explanation that would work for story purposes. But, if you want the most believable biological mechanism for animating a human skeleton, it's a human body. (Again, doesn't mean you can't get more daring for story purposes.)

Does the organism strictly have to be hidden inside the bone?

If not, consider a creature made out of extremely stretchable soft tissue that has evolved to a predator by attaching to hard objects, like rocks and sticks and use them as means of locomotion and for weapons to kill their prey and then dissolve the victim by encasing it in its gelatinous body.

Over the course of its evolution the organism realized that the bones of deceased mammals offer perfectly balanced and sturdy bodies and are already equipped with useful tools in the form of claws, beaks and teeth.

However, and this is not limited to this proposal, keep in mind that whenever an organism takes over a human skeleton, it will likely struggle to keep the body in balance, and might prefer to use it as a quadruped instead. It may even choose to not attach to a human skeleton at all and prefer simpler shapes of other animals.

Warning: I have no idea if this would actually work in real life.

Magnets.

You need something to hold the bones together at the joints. Barring externally-visible connective tissues, you're going to need something invisible. Fortunately, magnetic fields are A) invisible and B) all about pulling things together.

Take each individual bone and fill it up with machinery to produce and manipulate magnetic fields. Program them to interact with each other so that they'll link up with the other bones they're meant to be connected to, fluxing and flexing and reacting to what the other bones near them are doing. If you want to get fancy, throw in some radio transceivers so that the CPU in the skull can control the whole system centrally.

They're not organic, but I didn't see anything in your question that precluded robotically-powered skeleton monsters.