For now, a lot of the gig economy (but not all of it) is focused on non-essential services (food or other delivery, vacation rentals, private car rentals, etc), so in a time of crisis people can just stop using those services.
It will suck for the workers but even in a non-gig model that same problem would occur, although there would be more safety nets like unions and insurance ...
What worries me is if essential services start getting "gigged out" in a similar manner, that would be problematic..
Easy to say that would never happen, but "private citizens operating unregulated hotels/taxis" seemed impossible/illegal just a decade ago...