Steps to reproduce:
- Create a host with trigger in it. Add trigger to map as map trigger element.
- Move trigger into problem state.
- Disable host.
- In map trigger's label still indicates that trigger is in problem state.
- In map element's context menu 'Problems' item is inactive.
- Problem also is not visible in Monitoring -> Problems view.
- If same host added in map, it also shows no problems.
I assume that trigger should be disabled. Observations 2-4 might be correct.