I don't know if this is a common belief or something, but it is not true.

You can not die on other players islands. This includes the void. You can not die from falling in the void on others islands. Try it now. (/god mode off)

 

The only way I could see someone taking damage on other players' islands without being /trust-ed is hunger but thinking about how all other types of damage (cactus, fire, drowning in water, etc..) doesn't happen hunger probably isn't any different.

 

Some warp protections cut into peoples islands and you can take damage there but thats rares

 

Also, if you're falling off someone's island and do /home, you'll die. It's best to go somewhere where you're not a coop member or trusted to prevent dying :3

 

I believe unless a warp is overriding your island or if you're trusted, you cannot die at others islands'