TCP half-open
The term half-open, when referring to TCP connections, has two distinct meanings.
According to RFC 793, a TCP connection is referred to as half-open when the host at one end of that TCP connection has crashed, or has otherwise removed the socket without notifying the other end. If the remaining end is idle, the connection may remain in the half-open state for unbounded periods of time.
Nowadays, however, the term half-open connection is most often used to describe embryonic connections.