It's quite easy to put the ends of the tape back together with a bit of sellotape. Open up the cassette (sometimes there are little screws but it should just pull apart), use a pen to roll the loose tape onto the spool, cut a small piece of sellotape and put it on the table sticky side up. Then carefully place the 2 broken parts of the tape on it and fold the sellotape around.
I used to do it with tapes that had gotten tangled. But copy it on to a new tape then.