The official troubleshooting page for Pokemon Home now covers what happens if your Premium subscription expires after you've transferred Pokemon to Premium boxes, as Nintendolife observed, and the answer is fairly lukewarm news.
Pokemon Home Premium subscribers can store up to 6,000 Pokemon in 200 boxes, while free users can only store 30 Pokemon in a single box. As the Pokemon Company confirmed, if your Premium subscription expires while you have 31 or more Pokemon stored, you will only be able to check and transfer the first 30 Pokemon in your storage.
However, your other Pokemon don't disappear or anything. At the same time, you'll need to renew your Premium subscription to access them again, as boxes don't condense when you take Pokemon out. In other words, you can't subscribe to Pokemon Home Premium, dump 1,000 Pokemon, and then move them 30 at a time just using the first box.
Pokemon Bank, the handheld Pokemon transfer service which can now connect to Pokemon Home, has slightly different subscription protocol. If your Pokemon Bank subscription ends after you've used it to store Pokemon, you'll still be able to transfer your stored Pokemon to Pokemon Home by using Pokemon Bank as normal, at least according to this troubleshooting article. As a reminder, Pokemon Bank will be free until March 11, 2020 to celebrate the launch of Pokemon Home, so now's your time to move your handheld mon.
You can learn more about the differences between Pokemon Home base and its paid Premium version here.