a CKP sensor can fail in such a way - infact its the most common failure of a CKP sensor... this is why most CKP and CMP sensor fault codes are diagnosed at full engine temperature. This applies to both VR and hall effect type sensors.
anyway - in this case of the starter not spinning when hot, its a very simple diagnosis.
once the engine stalls out, immediately test the main battery wire for voltage drop - if that passes then check the solenoid for voltage drop, then check for good ground and respective voltage drop. If all electricals pass and all you hear is a click then - physically verify the engine is not locked.
If the engine is free to rotate normally with a ratchet on the crank then its highly possible the starter solenoid is bad.
Usually the culprit is found easily after a voltage drop test.
The bigger question here is what is killing the engine in the first place. The poster has 2 problems at the same time.