I don't know about other areas but I do know that a lot of counties/cities in California have services available to help pets of low-income/unsheltered people. No matter if it's a Social Services Agency, Animal Control (be wary of them but they can help), Health Care for Indigent/Homeless people, etc., many of the staff also love animals and will work with local vets, shelters, and other programs (e.g., Fix Our Ferals) to get these pets at least some of the help they need.
I do not grudge a homeless person, especially a woman, wanting to have a dog with them and I dearly hope she is able to reunite with her much loved pupper.