why can't he work? why do they only get £56 a week between them? I take it the flat they're in now is council owned and so nothing else payable, so the £56 is for gas/electric and food - that should be enough for 2 people.
Why don't you or your sister let him stay with you until he finds a job down by you and can then get a flat of his own? If the situation is that desparate, I can't see why this hasn't been done already - why rely on benefits? he'll just end up in the same rut as your mum...