Objects that are created from terrain have a netID starting with 1 ex. "1:-967887357", and are always local to everyone. From my testing, the Killed event handler as well as most others, will fire where the object is local.
Put these things together, and every client will run the event handler if its a terrain spawned object.
I created a server and 2 clients, found a random terrain object, added a Killed event handler on each client, then killed the object. The result is all 3 clients printing out from the event handler.
cursorObject addEventHandler ["Killed",{
systemChat str _this
}];
https://i.imgur.com/rnDV8Qt.png