Every incorporated city has a program and there are a few state programs. You can get a list of mortgage brokers who assist with these programs from the above linked site, I believe. If not you can get it from the San Diego Housing commissions site.
I am helping a family in El Cajon. We looked into this for them with a mortgage broker there. They can get up to a 30 percent “silent second”. It doesn’t “grandfather” out though (or it takes a very long time to do so).It involves equity sharing. There might be programs where the grants grandfather out and closing cost assistance too. There have been in the past. The equity sharing liability grand fathered out or wasn’t even part of some programs.
Normal ratios are used for DTI, 650 fico, 3 months pay stubs, w-2’s and 1% of purchase price in reserves “seasoned” for at least 3 months.. The seller can pay some closing costs including points.
The programs are based on the percentage of median income of the borrower and household size, among other things.