if I'm the money and someone else lives in it, does the tax break disappear

You can't share it. The exclusion attaches to the person who owned and lived in the home, and each owner's share is tested separately. So your half would be taxed and theirs might not be, roughly speaking, but the actual mechanics of how a co-owned residence gets split for this depends on how title and the ownership agreement are written, and that's a CPA conversation before you sign anything.

The reason nobody structures private capital around live-in flips is the term. Two years minimum, realistically 28 to 32 months from your wire to your payoff, with no interim cash flow because there's no rent. Price that as a loan and you're asking a homeowner to carry a hard money rate for two and a half years, which they can't afford and which a normal mortgage beats by a wide margin. Price it as equity and your return is a slice of a spread that might be $50k on a good day, minus the tax you owe on your slice. The lifestyle person is the one being paid here, in tax treatment and in housing they'd pay for anyway. There isn't a clean seat for outside money.

@sextant that's roughly where I landed too, and it's why I've stopped looking at this room for deployment. What I'd actually want is a second lien behind their primary mortgage, small, on a house they're improving anyway. But the underwriting cost on a $40k renovation second doesn't justify itself, and the borrower can usually get a HELOC cheaper.

@sable to your lender question, most residential lenders care about occupancy declarations. A non-occupant co-borrower is a thing that exists, but it changes the loan's occupancy category and terms, and those terms vary by lender, so you'd have to get it in writing rather than assume.

Worth separating the land from the house here. If you want exposure to the same neighborhood without needing anyone to live anywhere, buy the lot next door and hold it while they fix the house and pull the comps up. Slow, no exclusion, taxed like any other sale, but no occupancy problem and no partner.