My wife and I actually pulled this off here in Los Angeles County. We purchased a 4 unit property that was extremely outdated and moved into one of the units. We did a ton of work ourselves to make it livable and rent ready while living in it. We're actually looking as we speak for our next multi-fam to do this again.
It's challenging and will test your patience but it's worth it. Some of the best parts about this strategy is that we pay less living here then living in a single family home (rents increase every year) and when do decide to move out the place will cash flow and we've been here for 2 years.
When you do find a place you're interested in make sure to really understand who the current tenants are and what the rent control laws are for the city/county. Know how much you can anticipate raising the rents to each year as you're probably going to find listings that have rents that are way under market. You don't want to get into a situation where you move in and one unit has a nightmare tenant in it. Highly recommend Los Angeles County over City of Los Angeles.
Hope this helps!