[GRC]

You sound as though you want to harm the tape.

If you remove the power cable while the deck is running in play or record mode, and leave it that way for a while, the pressure between the capstan and pinch roller, where they grip the tape, will eventually deform the pinch roller, and leave an indentation in the tape. Short answer is 'don't do this'.

Removing an audio cable whilst the deck is running will not damage the tape in any way.

If you move the deck sharply enough, it's unlikely, but you could derail things enough to cause physical damage to the tape, but you'd really have to try hard to do so, I think. Again, the short answer is 'don't do this'

Does this help?