It’s actually already possible to subscribe to test runs even if the tests are not assigned to you. To do this you would just need to click the little email icon in the toolbar of test runs or individual tests:
While it’s not yet possible for an administrator to manage the subscriptions for other users (the users would have to click the email icon themselves), they would receive the email notifications for new test results, comments etc. It would theoretically even be possible to sent the notifications to an email list or email alias so the notifications get sent to multiple team members.
I hope this helps.