As Sumner says, there is nothing more abundantly clear: those workers who were permanently booted out of the workforce in America during the Great Recession aren’t coming back. And, yes, if those men wanted to work, they would be unemployed. And if employers wanted them, we would already be at full employment.
Note that the first failure of the male employment rate to recover was in the late 1990s, when the labor market was booming. The second failure was after the 2001 recession, which was much more mild than the 1980-1982 recessions. The third is taking place today. Those workers aren’t ever coming back. The pattern of descent proves it.