Easy fix.

Remove, or at least tighten the requirements, for welfare.

Your argument seems to be the equivalent of: if the (illegal? surely some of them) immigrants could get welfare they also wouldn’t do those jobs.

As welfare increases to the point where it starts to competes with jobs, it seems sensible to expect welfare will compete with jobs. Especially when you take in to consideration the expenses welfare recipients don’t incur as a result of not having to attend the workplace nor dress for such.