Follow up question: reading the relevant section of the NFL rulebook, it appears to note that a live ball foul by one team and a dead ball foul by the other still results in an offsetting penalty as long as it isn't a 5-and-15.
So as I recall seeing in an NCAA game earlier this season, A70 commits a facemask penalty and B20 commits a personal foul after the play. Both fouls are enforced so the yardage is a wash, but team A ends up with an automatic first down. In the NFL these just offset and the down is replayed?