Hi DeletedUser...
This is an interesting question, and I checked my own sandbox course to see if I could set a date to close self sign-up. Unfortunately, I didn't find any settings within any of my own groups (via the "People" page that allowed me to do this). So, I came back here to the Community site, and I found an open idea that someone submitted several years ago:
[Groups] Close self sign-up to groups on a specifi... - Page 2 - Instructure Community - 368490
I know this isn't a direct answer to your question, but you might want to read through the proposed idea and two pages of comments to see what people are saying.
Also, the voting process is going through some changes right now, so you'll want to read through this blog entry:
It’s Time for Your Feedback on the Future of Ideas... - Instructure Community - 619026
I hope this will be of some help to you...even if it's not a direct answer to your question.