In terms of workarounds, I'm not aware of any events that fire when you press on another tab, which would execute in-time to block the changing of tabs. (Anyone else on here? - I would be delighted to be proven wrong on this one)
However, what you could try is to do away with tabbed dashboard layout, and instead have a radio-button group, or several push buttons, to imitate the selection of different tabs, and these would drive a dashboard parameter which determines which cube view or dashboard component to display.
In fact one of my colleagues arranged pushbuttons horizontally in a way that looks like tabs, to get around some performance limitations with tabbed dashboards. With tabbed dashboards , when you open it it actually renders a lot of components that are in all the tabs, in one go, not just the tab that you want to display. So there is actually an upside to doing a workaround like this.
Once you have push button controls, or a Radio Button Group control , as the mechanism for switching between views, then you can put on the Save Action property = [Prompt to Save Data for All Components]
This should prompt for any unsaved changes before proceeding to perform the selection changed action.
It would be interesting to see if you notice any performance improvements this way, since by using this alternative approach only one view is being rendered at a time (unlike a tabbed dashboard that seems to process all components in all tabs even though it only displays one tab first).
