It all depends on the implementation. What you're describing is pretty common, particularly on blogs comment systems and YouTube.
This can likely be extended to only be utilized on part of a widget. If it's something like an ajax call you can easily add an option to cancel the request e.g. underneath a spinner.
For your report example in particular the service could be developed in such a way that the processing occurs independently of the user session. You can mix this in with an additional request which returns the actual progress of what has been calculated in the report such that whenever a user browses to that page, they can see just how much time there is to go before their report is generated.
This can likely be extended to only be utilized on part of a widget. If it's something like an ajax call you can easily add an option to cancel the request e.g. underneath a spinner.
For your report example in particular the service could be developed in such a way that the processing occurs independently of the user session. You can mix this in with an additional request which returns the actual progress of what has been calculated in the report such that whenever a user browses to that page, they can see just how much time there is to go before their report is generated.