If your opponents misses a compulsory jump that would capture one of your pieces and moves elsewhere ...do they forfeit that piece
That is an optional rule called the Huffing Rule.
Capturing pieces is compulsory. It is both players responsibility to make sure that is enforced.
It all depends on the rules you're playing - there are so many variants! In some variants, yes that would be the case (see the link).
It's advisable to agree the rules with your opponent before you start, otherwise arguments can ensue with no real solution.