Some people think that Elamite may have been related to the Dravidian languages, but as far as I know that hasn't been proven.
That does ring a bell — seems like some folks have thought they discern agglutinative structure in the very fragmentary surviving Elamite inscriptions. And you’re right, Sumerian was agglutinative. The Sumerians (who called themselves “the black headed people”, if memory serves) gave us cuneiform (possibly as a consequence of the agglutinative nature of their language) which really caught on as a medium for international relations in ancient times, peaking long centuries after the Sumerian and the Sumerians had vanished. There are no known relatives, living or dead, although it one looks around, there are some fringe thinkers who claim otherwise. :’)