Widget trigger for Workflow

Is there a way to trigger a workflow when a widget is signed? It would assign the signer role for a workflow to the e-mail used by the signer of the widget. Example:

New hire completes the widget for new hire documents on orientation site. Once he completes the required form fields and signs the document, it triggers the benefit form workflow and sends it to the e-mail address he entered into the e-mail field for the new hire documents widget.

I'm open to any ideas. I've been using two widgets but the inability to swap out documents when we change benefit vendors is creating a problem for me.