I'm a bit confused about the rule for 12 men on the field in American Football when it's called on the defense. It seems like sometimes this penalty stops play and the offense does not get a chance to run a play. On the other hand, offenses often try to catch defenses with 12 players on the field in an attempt to get a free play out of it. So why is play sometimes stopped and other times not?
This is common with the defense, because as you state, the offense tries to catch the defense with 12 players on the field. There are two different scenarios to consider with 12 players on the field (which is not always on the defense):
- The play is not allowed to take place when a team has more than 11 players in its formation.
- The play is allowed to take place (ie, the ball is in play) when a team has more than 11 players on the field of play or the end zone.
Rule 5, Section 1, Article 1 of the 2016 NFL rulebook covers this (emphasis mine):
The game is played by two teams of 11 players each.
When play is stopped:
If Team A has more than 11 players in its formation for more than three seconds, or if Team B has more than 11 players in its formation and the snap is imminent, it is a foul. ... In these instances, game officials shall blow their whistles immediately and not allow the snap or kick to occur.
When play is not stopped:
If a team has more than 11 players on the field of play or the end zone when a snap, free kick, or fair-catch kick is made, the ball is in play, and it is a foul.
I would have added this as a comment if I could have (not enough rep), but there is a key distinction between illegal substitution and illegal participation at the high school level (NFHS).
Illegal substitution occurs when that 12th man doesn't get off the field in time, but does not influence the play in any way. Illegal substitution carries a 5 yard penalty. (NFHS 3-7-5)
Illegal participation occurs when there are 12 in formation and they do all play defense, influencing the play. This carries a 15 yard penalty. (NFHS 9-6-4a) Here we kill the play if they are remaining in formation as it could become a safety issue.