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?
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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.