My mum isn't classed as low earner as she has state pension and works. The fact she has no money left at the end of the month doesn't matter it is earnings not outgoings considered.I'm sorry you and your Mum have had to go through all that. If anyone is getting pressured by the council to pay anything then they need to get proper legal advice. I honestly don't think your Mum could have been forced to make up the care package if she was low waged. They would have put a tie on the house but if she was over 60 then it couldn't have been sold from under her.
Like I say we were lucky to get CHC. So it was fully NHS funded. The fact we then had very little say in where he went or his care is another matter, despite holding POA for health and welfare. My dad died in October 2019 due to failings in his care.
Like I say dementia is the wrong disease. "Help" for those with dementia isn't forthcoming and even getting a diagnosis is painful