I've run into this before as well with another email service, so I get where you're coming from here. Unfortunately, if an inbox is full, you'll have to ask the senders of any emails to re-send the emails now that you've cleared up some space in your inbox. Depending on how their mail clients were setup, the email senders may have received a bounce-back email stating their emails could not be delivered, but this isn't always the case.
I know this isn't ideal, but it's similar to how your post office isn't able to continue stuffing a P.O. box full of mail if there's no physical space left in it. If the post office staff make an exception, or have a method for holding mail in this situation, then post office staff might hold the mail outside of your P.O. box somewhere else in the building until there is sufficient space to place it into your P.O. box.
However, most post offices don't have the space or proper policies for these provisions, so rather than risk the undelivered mail from getting lost, stolen, or otherwise mis-used, they'd return the mail to the sender, marked as undeliverable. The benefit to email is that an email client usually says why an email can't be delivered, while I know a lot of post offices just return mail as "undeliverable" without explaining why.
Just ask anyone who may have intended to send you an email while your inbox was full to re-send those emails, and they'll come through now, assuming there's enough space to receive them.
