Subvarsity game: Our association doesn't have a written policy for anything like that so it would be up to the officials at the site. If it was 2-person, I would definitely step in and help rather than have the game cancelled or finished 1-person. However, we have some officials who would not help out in that situation. If it was 3-person, I would ask the 2 officials remaining if they want to finish the game with 2 or if they'd like me to be their third for the rest of the game.
Varsity game: Again, no written policy.... however, I have had about 5 varsity partners injured since I started officiating and I have never had a "JV" official say no when asked to fill in.
I have always felt comfortable enough with at least one of the JV officials to ask them to fill in for the third official (another reason for JV officials to stick around and watch the Varsity game).