This strikes me as somewhat less of a problem than I might have thought:

We study long-run career consequences of initial employment in an occupation that subsequently declines. Linking the 2000 Decennial Census to US administrative employment and earnings records through 2020, we follow more than 2.4 million workers. Employment in an occupation that contracts by at least 25 percent is associated with about 5 percent lower cumulative earnings despite slightly more quarters worked. The earnings differential closely matches evidence from Sweden and Norway, although employment adjustment differs. Occupational mobility is substantial but incomplete, while children’s later occupational destinations are much less tied to their household heads’ 2000 occupational-growth categories.

That is from a new NBER working paper from