Here is a graph of the Fannie Mae mortgage serious delinquency rate and the unemployment rate since 1998 (ht @CharlieAllievo).
For the last two recessions, the delinquency rate and the unemployment rate moved in the same direction.
However, there were significant differences between the two periods. During the housing bust, many homeowners had little or no equity – or even negative equity – when prices started falling. If they lost their jobs, they were unable to pay their mortgage.
In the 2020 recession, most homeowners had significant equity – and the serious delinquency rate increased due to forbearance programs (most homeowners have exited forbearance now). Note: Fannie includes homeowners in forbearance in the delinquency numbers.
Following the 2001 recession, the serious delinquency rate didn’t increase significantly even though the unemployment rate increased.
I don’t think there is a clear relationship between the delinquency rate and the unemployment rate. It also depends on lending and homeowner’s equity position.