AdiIRC

Typically adiirc will show a disconnect error when a socket connection is terminated, otherwise it will fail to send a ping after about 60 seconds or timeout after 60 seconds. Do you see a disconnect error after about 60 seconds?

Ah, I never paid attention to waiting 1 minute.
There is no vent indicating that unreaircd (or another irc server) is no longer responding? as for example with socket.io on nodejs, there is a "close" and "disconnect" event, it indicates directly to the client that the server is cut off. Isn't there an equivalent with adiirc?

There is, and adiirc uses it, it usually works, but it's not always guaranteed to be instant.

Oh ok it's good I understood the thing, i have to manage a famous ping timeout, I remember that's it, I never know how to manage that even for smartphones especially quickly immediately for example. I struggle to do this

As soon as we cut unrealircd, there is really no vent indicating that the server has been cut? a sort of "Oops, unrealircd is stopped" or I'm confusing it with the Anope services

No there is not. It should as I said, detect the termination of the socket and raise a disconnect error, I don't know why it doesn't in your case, it works here.