It's already private, I presume you mean some form of restructuring the cap table so the founders/team have fresh ownership to work with.

A noble thought, but then what? skeleton crew the business at a snails pace while still being unclear how to actually make money?

His story on https://www.failory.com/interview/friday suggests it's making 10-25k MRR. If he can run it on autopilot with just occasional bugfixes and support queries, he's still got a very nice "lifestyle business" that will probably keep yielding for a couple years.

I think your idea fails for at least a couple key reasons. First, a lot of customers will probably migrate to competitor if they know the product isn't in active development anymore, so the MRR will likely drop over time. Second, investors are not going to just give up their equity while the owner directly profits off their investment, there would have to be some type of buy-back, and the owner probably doesn't have that kind of money.

25K MRR is enough to support a team of maybe 1-2 people, which probably isn't enough to answer all their customer queries, keep the infrastructure up and running and continue marketing efforts to ensure revenue at least doesn't go down year to year.

Gumroad successfully negotiated something with its investors and still exists and is profitable.

there are certainly numerous success stories. i have friends who "recapped" and went on to be quite financially successful, but that is likely the exception, not the rule.