When a client's INET socket is closed, the socket on the server's end will show up as 'ready', but the next read from it will read 0 bytes, or in perl's case as 'undef' if you read it with <$socket>. In the case of 'non-blocking' io, if you get a positive can_read() and read length of 0, then the socket was closed on the other end.

@reads = $select->can_read() ;
for( @reads ) {
   $data = <$_> ;
   if( $data == undef && $! != EWOULDBLOCK ) {
       # socket closed from the other end
   }
}
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Reference: Unix Network Programming 2nd Ed Vol 1 page 166-167, by W. Richard Stevens