The word static applies to the rigidbody components. There are 3 kinds of rigidbody components, static, dynamic and kinematic. Static are for things that do not move dynamic is for things that are fully managed by the physics simulation and kinematic are for things that affect other dynamic objects but themselves are not affected by them.
None of these change their shape automatically because of a skeleton. You need to do this yourself in code. For example you can add a child entity with a box collision component and then have a script that scales the collision entity depending on the aabb of the animated entity.