I recall that an 8-track player pulls the tape out of the center
of the reel of tape, and puts it back on the outer rim of the reel.
Thus, if you pull one inch of tape out of the center, the reel should
wind up two or three inches back on, due to the ratio of diameters.

So I would say that if the tape is not broken, you should be able to
gently pull tape out with your fingers, making sure to pull it out of
the same side of the cartridge that the player would, and this will
cause the slack to be pulled back into the case faster than you're
pulling it out.  Pretty soon it should be like new.

However, since the tape got "eaten", that implies the reel stopped
turning properly, in which case the cartridge may be messed up.  Unless
the tape got wound around the machine's capstan (as in a cassette
player), in which case your cartridge reel may still be OK and you can
use the finger-pulling technique as long as the tape is not badly
mangled.  Good luck.

Mike Knudsen