There are shortable futures contracts tied to US housing price indexes[1], but they're highly illiquid (rarely trade, and have wide bid/ask spreads). This is probably related to the difficulty of hedging, since as another poster points out housing is not fungible, and to the very high transaction costs involved in buying or selling the underlying.
Yeah I know about those. Robert Shiller was behind this project, in his mind many mortgages should be bundled with a put option on such an index. I agree. Needles to say his idea didn't catch on.
Here I was thinking about shorting specific homes, those for which one of the parent comments implied that their value is substantially lower than the current asking prices. It's a very futuristic idea, though not entirely impossible. If you're long on something then lending that thing out to a short seller is profitable because he has to pay you the lending fees (usually up to a few % per year).
Interesting idea! Who would take the other (long) side of the trade? Why would someone who thinks housing prices are going up not just buy a house outright?
The long party is whoever currently owns the property that is being sold short. It would be essentially a leverage tool for property owners. As a property owner you already enjoy a cash flow stream in the form of rent (could be implicit if you live in the property), you'd get a second stream from the short seller.
The only fuzzy part in this scheme is when does the short seller finally get paid. It would probably require some kind of a foreclosure on the property (otherwise the property owner would have to lock up a significant amount of some other collateral), putting a cap on the short sale profits.
This is kind of how reverse mortgages work. There the bank (or some other financial company) plays the role of the short seller, while the retiree is the long. The short side payout happens at death.
[1] https://www.homepricefutures.com/