When the user performs a batch operation, an overlay appears with a progress bar and a 'stop' button, that allows him to stop the operation before it ends. If the user stopped the operation when 10 out of 20 items were completed, should the confirmation message say something about the 10 that haven't been completed? Should I relate them in any way?
Stop the operation BUT give the user the option to see the items completed!
So yes you should relate them especially if the user can do actions on them and there is no requirement that is preventing you from providing it (i.e. business requirement). Here is an example:
This is the text in the image, I realized it is small after the answer is posted:
"Call this a batch that the user stopped before it finished running all items. The status is "Stopped", and then the icon under the Actions navigates the user to a pop-up or a page that displays all items, and provides some actions to the items that finished running.
When you say a Batch, it usually refers to a group of items. So you are running a group of items were some might be done before the others, some users might just want an access to the first few that are done running, some are doing it to test time consumed and see how many ran, how many has not when they stopped the operation at a certain time...etc Meaning users might have different reasons, so if the info is there and no reason to hide it, then make it available!
A best practice for this It will be discard all the changes if the user cancel the operation, the users should have almost all the power.
So, if you can revert the changes, just change the copy of the progress bar saying "Discarding changes..." while in the back, the files are recovering, so when everything finish, nothing will have happened, the user will be happy and relaxed.