The title says it all. Does this exist?
Well, one of mine comes close... Stack2RSS converts an API request to an RSS feed that you can subscribe to with an RSS reader. (You can also get daily emails with the contents of the feed.)
The RSS feed for tagged questions looks like this:
An example that fetches all questions on StackOverflow tagged
basic would be:
I don't know for how long the solution is around, making an app for that not needed anymore.
Just move your mouse over the tag, wait for the tooltip, press on Subscribe.
Only issue is that it is, just like any other e-mail notification on the system, not instant.