Direct evidence
This impressive collection of Los Angeles (and vicinity) city directories is housed online as part of the Los Angeles Central Library collection. When your elusive ancestor lived in L.A. only between 1920 and 1930, this collection can be a goldmine of possibilities. Not only is Los Angeles represented from 1875-1987 in this discontinuous collection, but there are scattered directories for Santa Monica, Watts, Westwood, and other communities.
The city was much smaller then, but the need to find housing outstripped the city's ability to provide it. So homeowners became landlords and rented out converted garages or rear structures for a monthly income. When someone's address is marked as, say, "1120 1/2 (r) E 22d" you know you're not dealing with a homeowner, and that it would be fruitless to search for property records.
David Stein is one such elusive fellow. He doesn't appear in the 1920 or 1930 census at any address we have for him. We don't know his age. We know he had a wife called Anne from a deed of sale, and we know that when the deed was processed he and Anne lived in the rear apartment at 1120 East 22nd Street in Los Angeles, a neighborhood then (as now) just a tad southeast from downtown proper.
In fact there are a good handful of David Steins from 1920 to 1930 living in roughly the same neighborhood, which was close to east-side Boyle Heights, then the center of the Jewish neighborhood. The illustrious Canter's Deli was there at the time and so were other Jewish shopping areas and synagogues.
One of the David Stein candidates, the one at 1366 East 21st Street, was a rabbi, a fact not revealed in this 1926 directory entry just above, but we know it from his declaration of intent to become a U.S. citizen. The same address was listed on his papers.
The David Stein at 1786 West 37th was a chauffeur, but he's not at the address we're looking for, so we can eliminate him as a likely suspect.
From the 1926 directory entry we know that our David on 22nd Street was a salesman, but what he sold wasn't revealed.
The sum total we know about our David: he rented a home at the address above, he was a salesman, he had a wife called Anne. But where he went after this brief appearance in Los Angeles is anyone's guess, for the moment. However, we managed to do what the client wanetd: to document his residence in Los Angeles.