If a synagogue member dies with no living family members remaining, who says the Mourner's Kaddish for them? Can anyone volunteer to say Kaddish for them?
From an Ohr Same'ach ask the Rabbi article http://ohr.edu/ask_db/ask_main.php/10/Q1/
Ideally the closest relative should say it. If there are none, a close friend, or in the case of a noted rav, one of his students. Technically, anyone can volunteer to say it.
In many synagogues I have attended, the rabbi is always saying Kaddish for someone who either has no family members and / or has family members but they are not religious, elderly, or for some other reason do not come to a daily minyan.
I am also aware of some organizations that pay people to say kaddish for others.