The private care provider says how much it will cost to accommodate her, including if they have to lease a building, hire and train staff, etc. They submit that bid. Many bids will be way out of cost restraints. Others might be acceptable to the people funding the care.
Look at other organisations that provide a public service (and social care is a public service).
- Royal Mail have a universal delivery obligation, which is why RM deliver to Highlands and Islands, Scilly Isles, etc when many couriers refuse to. What I'm suggesting as a transitional demand is that private social care providers have to offer care to all patients.
- The NHS have national rules as to when "expensive treatment" becomes "too expensive" Yet private care providers can pick and choose what to offer and turn down complex patients in favour of cheap and easy patients, and we've seen in this case how the NHS ends up picking up the bill for that. Again, a universal obligation to tender would prevent this cherry-picking of cases.
Social care should be nationalised, that's the definitive solution to stopping this cherrypicking, ending bedblocking (because it's all Govt money being spent, the Govt can increase social care places to accommodate people being discharged from hospital), and will also stop our taxes from ending up in the pockets of these care providers' shareholders.