It should not be beyond the wits of them to put their heads together and find some, even temporary, solutions. But if all they focus on is the strike action and how to look tough, nothing will be achieved.
The problems with delayed discharge is lack of care packages, so think "outside the box" reopen any possible sites such as recently closed nursing homes or put people into hotels. Offer care jobs at a good rate for a specified period of time, say two years with training given, at above minimum wage with flexible hours and maybe some sort of on site childcare.
If that doesn't find enough staff then ask if any of the migrants in the detention centres have caring experience and allow them to help out, while giving them accomodation in the same hotels.
They need a brainstorming session with nothing off the table.