I'm not the person you asked, but I do say things to strangers sometimes. It typically falls into two categories for me.
Compliments.
People who just seem as though they would like to talk.
Obviously category 2 is impossible to define in text, but so far I've been right when I think somebody wants to talk. All the people with whom I thought, "That person wants to talk," did talk a lot once I started things off with some random remark.
As to the compliments, people usually respond by telling me where they got the item I'm complimenting.
Then, of course, there are the actual crazy people, who do not need any encouragement in the talking department -- they always talk to me first -- but so far none of those ones have been assholes. I think my favorite was a lady who was having a loud argument with Jesus but then paused to say, "Bless you," and ask me if I needed a tissue when I sneezed.