I'm not aware of a listener like this in the JS API. If you are embedding the web authoring experience, you should check out this blog post: https://tableauandbehold.com/2015/12/04/embedding-web-edit-in-an-iframe/. Note that the process is able to 'listen' when web authoring is closed, which doesn't necessarily mean you have saved the workbook, but might be an starting point.
Hope this helps!
Yeah, that is not what I need.