Earlier quoted context omitted.
Personally, I'd hope the system would absolutely tell them "tough shit". There's got to be a line where the safety net gives out, because someone is too expensive to help. That's where family and charity hopefully take over. At the same time, I think your instinct is right, and it's something I've never heard mentioned before. It's almost inevitably that there'll then be the "food security" fund, and the "housing gua…
You could create basic income as a family of associated benefits. For example, give everyone a housing voucher. They can only spend it on housing, with the assumption they will need to top up from other funds It would still be "universal" because everyone has it and you don't suffer clawbacks.
If you stipulate that every family can spend an extra $1000 on housing, rent will go up by $1000 pretty quickly, and housing prices will go up by whatever $1000/mo in mortgage payments will allow.