"Letters from the government"
Since when does "the government" administrate individual benefit claims? If you mean letters from some other institution that is responsible for benefit related matters (there's more than one) and you were paying enough attention to remember the benefits being claimed, why be so vague as to say "the government" and not the correct department. It's not as if they don't have nice big easy to remember letterheads.
Council houses are administrated by the local council, not the government.
On another note, council flats are a right bastard to get let out, especially if high rise. No bugger wants them, not even benefits claimants. Councils up and down the country are either throwing them open to anyone who wants them (Google "no wait council properties") or decanting the existing residents before demolishing the whole block/estate.
There's an estate up the road filled with blocks of various types of council flats (high rise, low rise, maisonettes). Right on the estate they have shops, a primary school, launderettes, take aways, pubs, community centre, learning centre, church, ample safe free parking, green spaces with trees, wildlife and a groundskeeper. The local amenities beyond that are fantastic, huge shopping centre, library, council offices, cheap shops, dear shops, hairdressers, bingo, gyms, furniture & carpet shops, Royal Mail depot, doctors, late chemists, DIY shops, butchers, street market, dentists and the list goes on.
The flats themselves are oldish but nice, clean, dry, quite spacious with large balconies and the area is very quiet. My friends live in one and the view is breathtaking.
The rent is about £75 a week.
A large number of the flats are empty purely because they are council flats and people look down their noses instead of looking around the property. Every time one becomes empty, they are put on the "no wait" council list which is our local councils term for low/no demand.
So, if the OP's friend were to be dispossessed of her "cushy" council flat, there may be no one else willing to take it and I'd fail to see that another empty council property that's drawing no rent for the local economy as a good thing.