That means if everyone gets $1,000/month, then the rents go up by the same amount, which pushes prices of real estate and thus the mortgages. So after some period of adjustment, the money would be lost again.
I have not found an answer, but my gut says that it has something to do with the base of Maslow's hierarchy of needs. Meaning that UBI should somehow provide shelter, security and food.
It might be easier that it seems. Most nations already have monopoly on violence (police).
Food is more tricky. We already do subsidize farmers, so maybe this could be extended and basic food could be provided by the government (bread and such) or subsidized in full by it.
Shelter is the trickiest. There are some interesting cases across the World where governments have strong regulation around housing. One idea could be that every new development of multi-family housing or condos has to "donate" 10% of them to the municipality. These are then held by the city, that can "rent" it out to people who need them. They can't sell it. This would push the cost of these developments by 10% but it would essentially wipe out homelessness.
There are some ideas that I thought through over the years. As I said, I unfortunately don't have the answers.