This would be a problem of course, but I'm betting this is a problem most people would like to have. If my two options are: Die at 100, and not have to work for the last X years, or live an extra 20 years, with required working, I at least would prefer to live and work than to die and not work.
Since I don't think changing the lifespan will change societal values much, and because of that I believe that statistically the likely outcome is 'want to work but can't find it.'
Being at the end of your life and unemployed is a markedly different experience than being at the beginning of your life and unemployed.
