When the boomers die their homes will be bought up by private equity, same is happening to the supply now. Then they'll either sit on them to restrict the supply or charge ridiculous rents. I expect regulatory crackdowns will affect them before market forces do.
There was an article I saw a while back about a "young entrepreneur" who used his natural-born wealth to buy up a couple homes, then used rent collected on them to progressively buy up more. Eventually he owned the entire neighborhood and could charge whatever rent he wanted. It's a micro scale version of what's happening in cities like london and vancouver.