To survive in orbit around a WD is not a remarkable achievement - you just carry on orbiting forever (roughly). Orbiting a red giant would be pretty interesting, though - the RG has an indistinct surface, its diameter and luminosity varies, and it emits a lot of material as wind.
To survive in orbit around a neutron star would be another thing again. Neutron stars have intense magnetic fields, and spin rather quickly, resulting in a rotating field that is wrapped around on itself. That in effect creates a particle accelerator, driving electron flows (the electrons were all expelled when the NS collapsed) with extreme energies.
Short of hanging around near an exploding supernova, I can't imagine a more hostile environment.
I wonder what the band of survival is, where the planet doesn’t get turned to Swiss cheese first.
Yes, I get the "induction motor" idea. With fields and voltages that intense, I guess just about anything becomes conductive.
[Edit] I don't know whether those field strengths are consistent with atoms continuing to be atoms - I guess there must be some range beyond which a thing like a planet could maintain its integrity. But (guessing wildly) I would expect there to be a region around a neutron star within which it is impossible for atoms to exist.