That may be closer to the current number of 'non-resident' homeless. The figure I had for that is 23% - 1 in 4 - from 2015.
1 in 5 is the number of homeless (from the same survey) whose first place of residence in San Francisco was a homeless shelter. It's buried under figure 16 in this survey:
So 1 in 4 ( or 1 in 3) people are coming here directly to use the services. The 1 in 5 figure is significant because it strongly suggests that homeless nonprofits are actively seeking referrals from other parts of the state and country. We know that in some cases people are literally being sent here:
Yes, that was found to be illegal and some wrists were slapped. I find it hard to conceive that this is the only homeless bussing program - there's no other conceivable way that so many of them are arriving, and immediately finding places in homeless shelters that typically have waiting lists, and definitely have plenty of underserved former tenants.
Ultimately, the organizations involved have no incentive to stop referrals from other parts of the country. The more people they serve, the more money they can ask for from the city, and the more 'successful' they are as a non-profit business.
And just as serving more people is in their interests, so is dumping the most troubled, and consequently, most costly onto the streets in order to serving another round of newcomers. Once they've outstayed their welcome, or become too costly, they are shunted onto the streets. And the worse the crisis gets, the more money they can ask for from the city.
I'm not suggesting that this is some kind of intentional human trafficking. I am sure that (almost) everyone involved is doing so because, in a small minded way, they think that they are improving the world. However, the end result is a travesty.
My thesis is that our current environment is is the result non-profits being run in a capitalist business environment, with a capitalist, MBA-style mindset. Eventually, the business model achieves stasis with it's environment, which, in this case, involves letting the city be a dumping ground for human tragedy, and letting the city's tax payers pay $250 million dollars a year for the privilege. The crisis is the side effect of this expanding bureaucracy achieving homeostasis and justifying its existence.
It's more than 1 in 5, in fact it's almost 1/3rd of the homeless that have 'moved' to SF.