I've often asked this question myself.
I'm guessing they would suspend the season, hold innumerable memorial services, plaster the other teams' uniforms with stickers and patches, then allow the team to hastily assemble a squad of (for lack of a better term) scabs. Either that, or they'd simply cancel that team's season, give them a supplemental draft next season, and rearrange the schedule of every other team who was supposed to play the bereaved team that season. The interesting question is which team(s) would they choose to substitute for the bereaved team? If said team had been a divisional opponent, would they schedule a different divisional opponent to prevent tiebreaker problems? If the team had been in the same conference, would they schedule another conference team?
My theory is that teams scheduled to play the bereaved team would simply have a 15-game schedule, with tiebreakers being adjusted accordingly.
The NFL surely has contingency plans in place for such a catastrophic event. I doubt they'd be willing to make the plans public, however, so as not to give anyone strange ideas.
It still surprises me that entire teams travel together on the same plane. It seems to me that would make these planes attractive targets for deranged minds.
As George Carlin would say, "These are the kind of thoughts that kept me out of the really good schools."