How to reproduce:

1. Open the attached project.
2. Open Demo scene.
3. The cube has a script that enables all the Rigidbody constraints, waits one frame and then removes the constraints.
4. Press Play.

Expected behaviour: the cube should fall to the floor and begin rotating and bouncing relative to its rotation

Actual behaviour: the cube falls to the floor and comes back up without rotating at all

Possible workaround: destroy the existing Rigidbody component and add a new one.