Thanks for that info and choosing the Apple Support Communities. Based on what you stated, it seems you are experiencing issues with leaving group iMessage threads in the Messages app on your iPhone unexpectedly. If you haven't already, please force close the Messages app and restart your iPhone as iOS clears cached data and does other system optimizations when you turn your device off and on.
Force an app to close on your iPhone, iPad, or iPod touch
Restart your iPhone, iPad, or iPod touch
If you're still having this issue, your next step is to reinstall iOS on your device; this will help us isolate the situation further. Reinstalling iOS should not affect any of your data, but it is always a best practice to make sure you have a current backup in either iTunes or iCloud.
How to back up your iPhone, iPad, and iPod touch
Import photos and videos from your iPhone, iPad, or iPod touch
Once you have a current backup, follow the steps from the "If your device turns on but gets stuck during start up" section in this article:
If your iPhone, iPad, or iPod touch won't turn on
Use the “Update” option and not “Restore” and these steps will reinstall iOS. Keep in mind that these steps were written for a different issue, but they will still help us isolate the situation further.