The supervisor can also terminate its children. The communication goes both ways. But the children may also be supervisors with their own children. which all have their own termination behavior. The VM is designed around reliability and addresses this sort of behavior with language constructs.
Ok, I guess I'll have to give it a closer look. But are you positive they have a good story about interactions between hard and soft shutdowns? E.g. when grandparent requests a hard shutdown but parent a soft shutdown. Or vice versa. Or if timeouts of cancellations on different level of the hierarchy don't match?
It was designed for dealing with telephone switches, which could go offline for any reason, and need to be worked around. I recommend the entirety of LYSE, but [0] this chapter should give you some footing. To your specific question, upon receipt of the DOWN message, the processes can respond according to what makes sense to the domain.
