“2. If I’m not mistaken, zero down loans are usually constructed out of a 20% down first mortgage and a second mortgage/HELOC to cover the down payment. It’s done this way because 20% down waives the PMI requirement, interest on the second mortgage is tax deductible, and PMI is not.

In this situation, first mortgage is non-recourse, but second mortgage isn’t. Who lent you 100k to cover your down payment will try to sue you and collect his money.”
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You are mistaken as to the characterization of the 20% second mortgage as a recourse loan. It is not. It is purchase money and by CA law it is non-recourse. The lender has no recourse if you default other than seizure of the collateral. Doesn’t matter if the 2nd is called a HELOC or a Whozeewhatsit. It’s non-recourse.