At least via efm-oam you can have a dying gasp. 

You could probably add it to autonegotiation, by sending some symbol. There is already something similar in autonegotiation, like autonegotiation can inform the far end, when it is locally shutdown. That is, if I have A-B link, and B does 'shutdown' on the interface, A could emit syslog 'far-end administratively down'. This is supported by many common PHYs, but for some reason I've never seen software implementation. 

Of course this same thing 'admin down', could be abused by sending it always when you know you are going down. So an adventurous operator who controls their environment could add this today with just code.