And then, if you have proof of another habitable residence, you can get the cash value of all that instead.
The tricky part is that the austerity absolutely cannot reduce anyone below the minimum actual needs to live a full human life. You absolutely need to be giving them enough and healthy enough food, and water. The apartment can be claustrophobic, but it needs ventilation and sound insulation so people can actually sleep. The bed can be boring, but tall people can't be literally cramped when they sleep, and it needs to actually support their weight so people don't get back injuries. Health care needs to be fully adequate. Basically, minimum needs are 100% covered, so that if anyone ever wants to get working they don't have any immediate barriers. Don't take away anything that will make it harder for people to work.