Penalties committed after change of possession, offsetting rules?

Let's say the Jets intercept the Giants. On the INT return, Jets commit holding. If that is all, Jets keep possession, but take over 1st down 10 yards back from the spot of the foul.

What if after the INT, the Giants also commit a penalty, for example a personal foul on the tackle or tripping. Does the play not count and the Giants keep the ball? Is there any difference if the foul is after the play is over like unsportsmanlike conduct?