Can my boyfriend stay in Thailand until July 31 if he won't renew his work permit?

Both are technically invalid the day he finishes work.

The non-b is only valid with a WP. So officially he's meant to leave when the WP is finished or before that if his contract ends before. Remember taxes are due until he 'officially' finishes work.

Yes both need to be cancelled and if its your/his business the company needs to be closed and the companies bank accounts too. Tax receipts up until the end as well.

If he plans to come back with a proper visa as you say he is then yes it all needs to be cancelled or he is likely to have problems.

If he was leaving and never coming back he could just walk. But the visa needs to be cancelled even if he was coming back on a border bounce.

In short yes he needs to cancel everything officially the day he finishes work officially and leave Thailand.

You can get a 7 days get out of Thailnd 'extension' you apply and get rejected and get given 7 days.

I wish I could remember the order it all needs to be done.

Does he actually have a VISA or en extension of stay, because this makes a HUGE difference.