When Google closed its publisher portal two and a half years ago in response to massive ebook piracy, they said the move was temporary so they could "improve our content management capabilities and our user experience". Google has never fully reopened the portal to new signups (existing users continued to have access) but reports are coming in that the portal has briefly reopened on a couple occasions, and that Google is accepting indie authors on a case by case basis.
There's an ongoing discussion on KBoards about Pronoun shutting down. After hashing out the causes of the shutdown, the thread soon turned to finding replacements so authors could get their books into retailers.
Google Play Books was an especially hot topic given that only a few distributors could place a book there (PublishDrive, Ebook Partnership, StreetLib, to name a few). I was very surprised to read this comment on Google's publisher portal:
I can't give you specifics, but they have opened it at least twice this year. Both times it's been talked about here. And IIRC, it's been for short periods of time, as in hours, not days or longer.
I have yet to confirm that Google has had periods of open enrollment, but there are numerous reports that Google is letting authors sign up for a waiting list, and then granting them access to Play Books after a brief background check. For example:
For those who used Pronoun for Google Play, I highly recommend contacting Google Books and telling them the situation. I contacted them yesterday morning, received an email slightly less than 24 hours later with a link to fill out the Interest Form.
So, I filled out the form this morning with the hope that I'd get put on their "waiting list" and then get an invitation in a few months. Well I just got the invitation, less than 12 hours after filling out the form!
It may be a little extra work to get an account there, but it's clearly worth it to try.
That is just one of several similar reports I have found, so apparently this portal is not as closed as it would appear.
Google had a massive piracy problem at one time (it was about as huge as Kindle Unlimited's ongoing issue with scammers). It looks like Google's solution is to vet each applicant and only accept the ones that demonstrate their legitimacy.
Approving users one by one is a lot of work, but it seems there is no other option. Neither Google nor Amazon have found algorithmic solutions to their respective piracy and scammer problems, which means they may have no other choice but to have a real person deal with the problem.