Rats have a regular skeleton similar to that of a human or other animals like a dog or cat. The belief that rats do not have bones or have a collapsible skeleton comes from the fact that rats can fit into tiny places and walk through small holes.
A rat can fit through holes with a small diameter because of the oblong shape of its body. A rat uses its whiskers to determine if a space is too small. The rat does not collapse its bones but rather squeezes its body through small spaces. Rats with a larger circumference will not fit through small spaces.