Care refusal - a public law puzzle

Imagine a situation arises that a person, let’s call him Albert, has growing care needs, and the local authority (having assessed those needs) feels that the only way that all his eligible community care needs can be met is through a placement in a residential care home. There are variations on this situation. It might in theory be possible to support Albert through increasing his home care visits, through overnight support, but this would exceed the resources the local authority is willing to spend on Albert’s care, given that they can (in the authority’s view) be met by the (cheaper) care home placement. There are other variants – a person might be currently in the care home and wanting to return home. A young adult moving out of the family home might want to move into supported living (with their own tenancy) rather than a care home. All have in common two theoretical alternatives: a care home placement which meets all of a person's assessed eligible needs, and living in their own home with some unmet eligible needs.  Now supposing Albert does not want to live in a care home, he wants to live in his own home. What happens next?