Metal sleeve around cassette player motors?
It's a mu metal shield. This is a special material that 'conducts' low frequency and static magnetic fields very well (but saturates at a low field strength). The basic idea is that any small residual field generated by the motor magnets gets shunted through the mu metal rather than propagating out into the air around the motor and interfering with the tape reader head.

Mu metal has a relative permeability around 25x greater than soft iron, so if they wanted provide the same amount of shielding using the motor body, it would have to be roughly 25x thicker than the thin strip of mu metal.