Well they are leaving them vacant. Both rentals and houses across the country are sitting unfilled. NYC has anywhere from 13-26k rent controlled apartments vacant. As of last year ~16 million homes were estimated to be vacant overall and increasing interest rates have likely increased that. Why? Because these large orgs have purchased them via debt and it's just a line-item on a spreadsheet to them. Just build might work in a world where market actors were wholly rational and the government regulations actually targeted these perverse incentives, but that's not the reality we currently find ourselves in.

Why "Vacant Homes" Won't Solve the Housing Crisis - https://www.youtube.com/watch?v=3xZXdXxYBGU

Vacancy rates aren't generally increasing though. Vacancy rates are lower now than in 2003 by a good bit.

https://www.census.gov/housing/hvs/current/index.html