The vast majority of private trackers do not have a "hard" ratio economy like you describe. Most private trackers are flexible to give users ways to increase their own upload ratio without requiring that ratio to be "paid" by another user doing the downloading. e.g. when torrents are freeleech the users get to download for free but can still upload to improve their own ratio. And when there's bonus systems in place those bonus points can be used to add to the user's own uploaded data count. And sometimes private trackers have events where they make the entire tracker, or entire categories of torrents, freeleech so a whole ton of users get to download for free and will still be able to seed those same torrents afterwards.

does that mean that there are some users who will forever be below 1, and thus end up getting kicked out, thus resulting in the private tracker just… shrinking over time?

Sure, that could happen too. Private trackers will always get some users that just aren't going to cut it and eventually lose access to the tracker. In most cases the tracker will just end up adding new users and maintain the total user count. Each tracker is going to be different in how they approach this.. I think over time the user churn doesn't happen as much, at some point there's enough users on the tracker that are doing fine with ratio and whatnot while the tracker hits its own maximum user count so actually needing to replace users with new signups becomes less of a priority.