Ssh duplicates FILENO_STDOUT and FILENO_STDERR, thus there are two descriptors for each of those files.  When the remote program closes its stdout or stderr, the remote sshd sends the appropriate message to the local ssh which responds by closing the duplicate descriptor, but the original descriptor remains open.  A program reading from ssh's stdout (or stderr) cannot tell that the remote program has closed the file.

This is what should happen:

$ sh -c 'exec cat >&- 2>&-; sleep 5' | { read s || echo eof; }
eof
[then 5 second pause]

This is what happens using ssh:

$ ssh localhost 'exec >&- 2>&-; sleep 5' | { read s || echo eof; }
[5 second pause]
eof