Given a bit of practice, it is not impossible to totally disassemble potentiometers and put them back together again.
They usually have tabs that you can bend back and get the thing apart.
During this process you mostly find out why the potentiometer could never work again, but occasionally you can clean and furgle it without damaging it too much, and it will work again.
It's best to mark or photograph the parts before and during disassembly, as often there are multiple ways to reassemble it, only one of which is correct.
Since you have nothing to lose, I would give it a go and learn something.
Edit: Oh, and definitely try soaking it with De-oxit etc first if you can get it in there.