The HB should go to the landlord then. And the council should never be able to pursue the landlord for rent monies the tenant claimed fraudulently or was not entitled to.
I think the council should have a max of one fiscal year to catch out overpayments and what not and beyond that, tough, in general.
As for HB and working poor, we've had to claim partial HB in the past.
And tbh, it's the working/FT employment that's the issue.
It's not been a problem to find a landlord to rent, even 'No DSS' ones, if you can prove you are working FT and in receipt of partial HB.
The other issue is, too, if a person is in work FT, they'll be out of the house a good part of the day, so less wear and tear.
The other is that, I'm just guessing here, when you work FT you need to sleep to keep your job and probably can't turn up drunk/on drugs, so it's less likely you'll get a tenant with anti-social behavioural issues.
We can never afford any property, but I'd never touch BTL in a million years.