Ethics of soliciting letters for US permanent residency application?
For me, the key criterion is "do I know the person through shared endeavor" e.g. having studied or worked together for a reasonable period of time.   

If there has been no previous contact i.e. a stranger, I would NOT respond at all to a request for a support letter.

As a possible comparison, a stranger asks you to guarantee a bank loan for them ...  most people can see where that one will lead...