The res care can of course advise the person not to do it, but you said this which is incorrect
"if they discharge you before they think you are fit enough to be on your own, the fault & responsibility goes back to the Caring home if something happens that's when the legal side comes into it, " Claims" I doubt they are going to go down that road’”
The care home has no responsibility if a resident, who has the capacity to decide, chooses to leave and no successful legal claim can be made.
Reputation is, of course not so tangible but I think that any care home who made any attempt to prevent a resident from leaving, which is against the law, would be in far greater danger of damaging their reputation. Given that it could amount to abuse, whatever their views on whether the person can manage or not, they would be well advised not to try it!