Gas costs are significant expenses when you only make $1300 a month.
Especially in this case where the end result was that she ended up just crashing on her daughter's couch, moving down to Olympia or whatever to rent out some questionable super cheap room somewhere seems like it would have been a much worse decision. Perhaps she was just waiting long enough to justify "giving up" and having to rely fully on her daughter.
Why are you so defensive about the mere existence of a homeless person?
Her life has situations we cannot see from this perspective and we have not lived through. It's unhelpful to discount her situation with a smug "She could be doing XYZ better".
In the absence of such details, the article is basically just vaguely pulling at heartstrings.