If a private lender funds a live-in flip, what happens to the exclusion?

You cannot 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. The actual mechanics of how a co-owned residence gets split for this depend on how title and the ownership agreement are written, and that is 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 wire to payoff, with no interim cash flow because there is no rent. Price that as a loan and you are asking a homeowner to carry a hard money rate for two and a half years, which they cannot 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 owed on your slice. The occupant is the one being paid here, in tax treatment and in housing they would pay for anyway. There is no clean seat for outside money.

@dpatel_re 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.

@chriswalton8 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. It is slow and it gets taxed like any other sale with no exclusion, but there is no occupancy problem and no partner.