If rates go up like that the housing market will freeze up and people wont sell if at all possible to avoid.
Banks who own the assets if they force people to sell don't want to see the asset values go down below their collateral required. Hence banks move softly and let the majority of underwater people ride it out instead of selling.
If rates go up, there would be massive liquidations all across the board. Landlords with 12 properties would have to scale back to survive. Those properties would be sold for fire sale prices. Fire sale priced homes are not going to rent for a lot of money. Bonus; it will totally bankrupt Blackrock. Rates will go up if we are lucky enough to have a world in which we will be in it.
Why would rents go down? It might go up?