Jira allows to structure issues hierarchically by using links between any kind of issues (tasks) as well as parent/subtask relations. But there is no further functionality implemented that a neither a subtask nor a linked issue/task can influence its superior task and vice versa.
The catWorkX JIRA Transition TriggerFunctions app provides a collection of post-functions where a transition of one Jira issue can trigger a transition of another Jira issue. For example, if the superior task enters a certain state, a transition is performed on sub- or related tasks. Additionally, you can limit this transition to defined (sub-)issue types.