Well, considering that every homeless census of SF shows[1] that the vast majority aren't long-term residents of San Francisco and that SF has some of the most renter-friendly laws in the country, I'm going to say "not many".
[1] If you understand how statistic work, and how to read critically. The censuses seem to be written by someone who thinks "How to Lie With Statistics" was an instruction manual, not a warning.
Edit:
Here's the latest pre-pandemic census: https://hsh.sfgov.org/wp-content/uploads/2020/01/2019HIRDRep...
On page 18, we learn that fully 30% of SF's homeless became homeless before moving to SF.
Of the remaining 70%, only 55% (so 38% of all homeless in SF) are long-time (>10 years) residents of SF. 27% of SF's homeless lived in SF between 1 and 10 years.
On page 19, we learn that only 30% of SF's homeless had a home they owned or rented immediately prior to becoming homeless. The rest were couch surfing, institutionalized, in SROs or subsidized housing.
We probably shouldn't assume zero correlation (but we don't have a better prior, because the crosstabs are not available, so...). But if we do, this suggests only around 11% of SF's homeless population were long-term renters who were kicked out.
On page 22, we learn that only 13% of SF's homeless cited "eviction" as the primary reason for currently experiencing homelessness. In contrast, "lost job" is the the most common reason, at 26%. Substance abuse is #2 at 18%.
On page 21, we learn that 65% of homeless people in SF have been homeless for more than a year.
That's an interesting statistic because that's the same percent homeless who became homeless while in SF and whose total residency in SF was more than a year. Again, the crosstabs are not made available to us, but it is suggestive that many of the people from page 18 who reported being long-term SF residents were not long-term SF residents at the time they experienced housing loss.
Not to sound conspiratorial, but my points above could be easily refuted with crosstabs from the census. The silence is deafening.