Since this is an old question and since this does not currently have a right answer I will summarize this.
- All rule requirements for players on a field beyond 7 players on the LoS on offense are league mandates and bylaws.
- Every league has its own bylaws and subrules and these are often not publicly available or they are just "spirits of the rule" where commissioner decides.
- No game is over until the last play is finished.
- If a football team left the field before a game was over (even for one play) they would be under heavy scrutiny and almost certainly sanctioned by the league they are in.
- The referees using league bylaws have the discretion of making decisions on the field.
What this means is that the referee could require a few players or 11 players to be on the field on defense. If a team refused to do whatever the head referee asked then the game would end in forfeit (it happens in college and high school - not often but happens).
I can tell you right now that if an NFL team ends a game in a forfeit it will include sanctions on that team up to the owner. Any NFL team can leave the field and pout about whatever. There is no "rule" in writing against this. But it would probably include one of the most drastic penalties ever (draft picks, money, ownership suspension, coach suspension...).
So to be clear the answer is - a team has to field whatever number of players a referee determines to be the minimum on the field or the game will be a forfeit.
For 2019 and later rule 4-8-2c was added so that the game can end
without the PAT attempt taking place.
Patrick is right in his answer on this. However the interpretation has nothing to do with the question. The question is, "Does the defense have to defend the extra point?" Rule 4-8-2c is a rule that allows the offensive team to skip the extra point after the game is over. It has nothing to do with this question - at all.
If the offense decides to take the field the defense is required based on the bylaws of the league to field a team or they would be forfeiting the game. As I have mentioned the forfeiture of a game is probably so steep of a penalty compared to getting your guys on the field that it would just never happen in the NFL.
Rule Specifics -
- Patrick did a good job answering his own question here - Is there a minimum number of players needed on the field in the NFL? . Yes referees would not alter a game if a team forgot to have players on the field for a game - had a play or two with 9 or 10 players. But if a team on purpose did not field players, the referees would invoke the rules talked about in this question/answer.
- https://www.cbssports.com/nfl/news/nfl-week-6-grades-browns-get-a-d-for-blowout-loss-to-steelers-packers-get-an-f-for-ugly-performance/ and https://en.wikipedia.org/wiki/Unfair_act#:~:text=Under%20Rule%2017%20of%20the,onward%20and%20resume%20play%20from. Both of these talk about Rule 17 which is basically an umbrella rule that covers anything not in the rulebook because literally they would have to write a couple thousand more rules to cover anything that could happen. Also most of these rules would be for acts that are so bad that no team in their right mind would do them - trying to hurt someone, jumping offsides over and over, ejected player not leaving a game and so on. Try finding a rule for these things which are obviously not legal.
- There is another rule that should be looked at here - http://static.nfl.com/static/content/public/image/rulebook/pdfs/16_Rule13_Non-Player_Conduct.pdf. If it were a playoff game there really wouldn't be a way to enforce something, that being the refs adding more points to a score or game... However the refs (probably consulting with the commissioner's office) would have the ability to add points to a score which could effect playoff seeding.
- What would actually happen is this
ARTICLE 3. PENALTIES FOR UNFAIR ACTS The Commissioner’s powers under
this Section 2 include the imposition of monetary fines and
draft-choice forfeitures, suspension of persons involved in unfair
acts, and, if appropriate, the reversal of a game’s result or the
rescheduling of a game, either from the beginning or from the point at
which the extraordinary act occurred. In the event of rescheduling a
game, the Commissioner will be guided by the procedures specified in
17-1-5–11, above. In all cases, the Commissioner will conduct a full
investigation, including the opportunity for hearings, use of game
video, and any other procedure the Commissioner deems appropriate.
So walking off a field would be enforced by the commish. I am sure at the very least it would include a heavy fine. If it were done in an extreme way it would probably also include points added to the other team or loss of draft picks or alont those lines.