End Of Stream means that the client closed the connection (from the point of view of the server). The server then tries to cleanup by closing the socket explicitly, in some cases that results in debug messages you see.
EndOfStreamException: Unable to read additional data from client sessionid 0x0, likely client has closed socket
Notice that the session id is 0 - so either this is a zk client that failed before establishing a session, or more likely it's a monitoring command (which never establishes a session (working as designed)).
There is nothing worry about here and this is normal behaviour.