Since US life expectancy is just under 80 and doesn't seem to be in any danger of going much higher, I doubt that the full retirement age will be set anywhere near that. I suppose it could increase by a year or two but that would presumably be done gradually as the last increase was.
Also, what seems more likely than complete collapse is that Social Security benefits could be reduced or grow less quickly and that Medicare could become more expensive. Medicare costs are already higher for people with higher incomes and it has been suggested that Social Security benefits should be means-tested as well. Whatever happens, Social Security was never intended to, and never has, fully funded retirement.
Having said that, any change at all in these benefits is a third rail in US politics. So the whole can could just be kicked down the road again while the US sells more T-bills for as long as it can find willing buyers.