I don't think long-term unemployment among people with a disability or other long-term condition is "fantasticaly rare", sadly. This is not the frequency by length of unemployment, but:
https://www.statista.com/statistics/1219257/us-employment-ra...
I've worked with a contractor that went into a coma during covid. Nearly half a year in a coma, then rehab for many more months. Guy is working now, but not shape.
I don't know the stats, but I'd be surprised if long medical leaves are as rare as you think.
(A seriously underrated statistic IMO is how many women leave the workforce due to pregnancy-related disability. I know quite a few who haven't returned to full-time work for years after giving birth because they're still dealing with cardiovascular and/or neurological issues. If you aren't privy to their medical history it would be very easy to assume that they just decided to be stay-at-home mums.)