Do rats have a collapsible skeleton? Do rats have a skeleton made entirely of cartilage?

No. These are myths.

Rats have a skeleton made of bones connected with joints and cartilage, just like we do.

These myths may come from the observation that rats can fit through some surprisingly small holes, and that a fleeing rat moves with an extraordinarily fast, fluid gait. A rat may appear to swarm along the bottom of a wall and wriggle like an eel through a small hole.

It may be tempting to think that the rat must have bones that bend or come apart to enable it to perform such feats. But this is false. Rats have the same kind of skeleton that we do.

Rats can fit through some surprisingly small holes, but it isn't because their bones are soft or come apart. Rats can fit through small holes because their bodies are long, flexible and cylindrical in shape. They are burrowing animals that spend their lives running down tunnels and through tight spaces.

Rats determine whether they can fit through a hole using their whiskers. A fleeing rat makes this judgment very quickly, by just poking its nose into a hole and dashing through if it is large enough, and darting on to another one if necessary.

Note that an overweight rat has different proportions from a healthy one: overweight rats tend to put on fat around their abdomens, leading to a large girth and an inability to fit through holes as small as those a healthy rat could fit through.

Small rats can, large rats cannot.

A quarter is just under an inch in diameter (0.96 inches). Not all rats can fit through a hole the size of a quarter. Large rats and overweight rats are too big. But some rats are small enough to fit through -- especially juvenile rats.

The smallest diameter hole a small rat might fit through is an important consideration when rat-proofing an outdoor structure against wild rats, and when choosing a cage which will house baby rats. Generally, wire mesh with 1" x 1" holes is considered too large a spacing for young rats, while 1" x 1/2" and smaller dimensions are narrow enough to keep even the smallest rats inside. For rat-proofing an outdoor enclosure the recommendation is usually 1/2" x 1/2" mesh or smaller.

Yes, occasionally.

I have seen it happen once myself. Two of my rats, Widget and Snip, were in a cardboard nestbox together. They got into a fight -- I heard the shrieks and thumps and saw the box shaking and bouncing. Then Snip darted through a hole I had cut in the roof of the box. But he got stuck! His head, shoulders, and the upper part of his trunk fit through, but his lower belly and hindquarters would not fit. Snip's hind end hung exposed and vulnerable to Widget, who was still in the box and who was presumably pressing the attack from within. Snip screamed and flung himself so rapidly back and forth that he was a blur. After a second or two he reversed direction. His head and shoulders disappeared back into the box and he shot out of another, larger, hole. The entire episode lasted about three seconds and was over too quickly for me to intervene. After it was over, however, I removed the box and enlarged all the holes.