Someone will pick up the rights to show the games, or the league will offer their own service, or the games won't be played on Mondays/Thursdays and will go back to just being a Sunday sport.
Regarding losing their audience and destroying their value:
I stopped following the NFL not because of politics (the kneeling thing hadn't yet started), but because their product was no longer worth my time. Thirty+ years as a fan, watching nearly every single game the local team played and I turned it off a couple years ago. It should not take 3+ hours for 60 minutes of "play", the bulk of which involves no action. It became so overloaded with commercials that it hit the point I was no longer interested. For a short while there was hope, they had the "game in 60" replays on the NFL network. That could have been amazing. Unfortunately, they screwed that up too, showing "all the action" in the first half (good!), then a shortened version of the halftime show (why?), then "all the action" in the third quarter (good!), and then they'd jump to the end of the fourth quarter (wtf?). Why did we need a halftime show when the whole thing a) is being condensed down to an hour, b) is a replay, and c) they sacrifice showing comebacks in order to bring us talking heads?
I think they've been losing their audience for a while; the politics is just the latest (and possibly biggest) factor in their decline. If they turn things around, great. If not, I won't feel sorry for them.