They do. My husband's auntie has a council flat. Last year her friend had a heart attack abroad, but wasn't fit to fly home. Long story short, lots of pissing about by the insurance company and in the mean time he deteriorated and ended up passing away over there. Proper shocker as he was really healthy and active. His long term partner, was in a right state. She's a perfectly capable woman in most ways, but the shock and the grief of it just knocked her. My husband's aunt ended up staying with her for a while as she was trying to sort everything out. There was a right faff with repatriating him, getting a death certificate, etc., as they'd been together for 40 years but were unmarrried. So she stayed, helping her and looking after her and her three grieving dogs, for a few of weeks, went home for the odd night and then went back to her friend's.
Anyway, a neighbour reported her to the council. Someone popped round and asked to come in. They did briefly and then said, Oh! It's fine, we don't need to! Basically, they'd seen her living room and kitchen, saw the Christmas decorations, and saw that the flat was clearly being lived in, or sublet
So, if someone shops the daughter and someone comes round and there is no sign of the daughter or her child(ren) living in the property, just her brother, then that's the risk you run.
If she buys with her husband, then does she go on the mortgage? If she does, will she have to declare her rent for the mo ths that she will be pretending to live there? That will impact affordability. If she doesn't go on the mortgage, as an adult occupier not on the mortgage, she will have to sign a waiver as an adult occupier. Looks weird if they are married and they say that she isn't living there.
Lying to your mortgage company is mortgage fraud. If caught out the lender could request immediate repayment of the mortgage and getting a mortgage may be impossible if you're blacklisted. You could be fined and go to prison for upto 10 years.
Lots of lies at lots of different levels and lots of unneccessary risks if the end goal is keeping a council house. They risk losing both and not getting another.