Mangled tapes?

I have a large collection of video tapes of programmes and films recorded. Recently, when winding the tape back, on quite a few occassions, after the tape is removed from the machine, the tape is exposed for about 6 inches and mangled, which always happens at the end of the rewind.
Can somebody advise me as to what the problem may be.
I really don't want to have to change the unit, as it also has a DVD player, and suits me perfectly, but I don't want to damage anymore tapes.
I purchased good quality TDK tapes and tried them, but once again, it has happened.