From a jira-user post:

The guys here have grumbled quite a bit about the inability of Jira (out
of the box) to notify people when other tasks they are blocking become
resolved. I was thinking last night about this (hey shouldn't it be just
the Jira developers who dream about it?!) and was reminded of a simple
solution I've thought of before:

Add a notification event for "Linked Issue Resolved", and a new
notification target grouping "Assignees of all linked issues"

This event would be triggered when any issue that is inwardly linked
(linked TO by other issues) is resolved, and notifications, if setup
usign the new notification grouping, would be sent to all Assignees of
the inwardly linking issues. Hey presto you find out when issues you
depend on are fixed.

This is loosely related to some of the ideas in:

http://jira.atlassian.com/browse/JRA-2678

Workaround

As with all Automation rules, please keep in mind your Automation Service Limits.
There's now a very easy way to notify people watching linked issues using Automation for JIRA! Available for both Server and Cloud.

You can create a rule that comments on linked issues when an issue is resolved. JIRA will then notify the watchers, though you could also set Automation to email, hipchat, slack or text the watchers as well.

The rule would look something like:

This was done as part of work to make related issues easier to work with. For more details see https://blog.codebarrel.io/synchronize-parent-and-sub-task-issues-with-automation-for-jira-bdcca6c9d453