POSIX doesn't provide a way to find out if the other end has closed a socket without attempting to read (EOF) or write (connection reset etc). Linux 2.6.something added POLLRDHUP to detect that, and by now it's fairly widely used. It's a bit like POLLHUP, but it fires when remote shutdown(SHUT_WR) or close() sends a FIN, not only on errors/full-shutdown. At least illumos has also adopted this flag.
I am not sure what visibility the flag should have (__BSD_VISIBLE) or whether it should be in POLLSTANDARD.
Random examples of users of this flags in the wild (I happened to write one of these):