ok, if a connection is not "closed" - but rather just "lost" then neither side is notified. In this case both sides can still "see" the connection - it'll only generate an error when you actually try and use it.
Bear in mind that connections are not "physical". They're just stuff in data at both ends. So when a "connection" is established, it's not like some physical line is drawn between two points. It's just an "agreement" of both sides to configure some internal data structures in a certain way. "Closing" a connection is one side telling the other that they're done, whereas "losing" a connection is some physical thing that happens between them, which neither can detect.
Some protocols institute timeouts, or "heart beats" to check if the connection is still valid.
cheers
Bruce