As AutoSlash said, there's usually a buffer, albeit a very small one. Some customers don't show up, which releases spare capacity. Other times, cars randomly break down, even on a sold out day in a market experiencing their peak season. In a few cases, an elite status customer reserves at the last minute, on a contract that allows guaranteed availability with a certain number of hours advance notice.

So when the rental company stops taking reservations, there may still be a very small number of "extra" cars left. But not enough to write a research paper on, if that's what you were hoping for.

Think about it this way. Imagine you're having a birthday party. You expect 25 guests. You will probably order a little extra food, maybe for 27 people. Too much more, expensive food gets wasted. Where it becomes a problem is when you try to be clever and assume 30% will no show, so you order 30% less food, to save money. Then, big shock, everybody actually shows up, meaning some people won't get to eat. Judging by more frequent sell-outs in large markets, I wouldn't be surprised if rental companies are increasingly trying this tactic.