Dynatrace by default alerts on hosts and VMs that shutdown or restart in a non-graceful way or if network connection to the host is generally lost. Dynatrace by default does not alert on graceful host shutdowns (but that will be introduced as a an opt-in in the upcoming release two weeks from now).
If you would like to explicitly alert on process shutdown you have to opt-into process availability alerting that also works for clusters of processes and min. number of instances running.
See the help documentation here: