Okay, you offer help, the person tells you to fuck off.
Very few mentally ill people realize they need help.
Very few mentally ill people realize they need help.
And every month or so hose it off for him.
The percentage of people who would actually continue to do so is small, but would be provided for. Anyone else in a similar house could just use the toilet.
I think OP was trying to get at the sad reality where severe mental illness is treated with some sort of loss in agency. You're still forcing some sort of solution they may not want and may work to sabotage.
You could advocate for encompassing services (e.g. regular visits from a nurse) but you'll quickly arrive at modern psychiatric facilities if for no other reason than scale and cost.