It would just stop at that point, however you also don't say if you might have Paused the scan as you later mention about it scanning the same files 3 times.
You don't say what version of avast you have ?
The Home version requires interactive input by the user when a detection is made, you need to decide on what action to take, move to chest, etc. and avast then carries out that action and continues with the scan. If you then stop the scan previous actions have already been actioned.
When you start the scan again (if not paused) it doesn't remember where it was before (it doesn't retain that information in the home version), so the scan starts anew. If you paused it then as far as I'm aware it would restart at the same folder.
Why would you want to stop the scan ?
