Have features push a status to a field in Jira when deleted

As a product manager I would like the ability to keep track of which items in JIRA/AHA have been deleted in each system. I know Aha! will not likely implement a feature to delete issues in Jira when respective items are deleted in Aha! However it would be useful to be able to automatically push a status or field update to jira, so users working in Jira can easily see items that have been deleted in aha and vice versa. It is currently messy to track, and we have literally redone integrations rather than try to clean up/constantly keep it clean.