If a file is deleted, it will show up in Recuva. If it is erased, under normal conditions it will not show up in Recuva. Your switch-off created abnormal conditions, and therefore it made sense to see if anything was recoverable, even if it was not visible in Explorer in the normal way.
Switching off without shutting down properly can certainly corrupt files, but it does not happen invariably. Again, Recuva may help.
I don't know what order Eraser deletes files in, but would assume that it is in the order in which the file names appear in the task definition, which is the order in which they were added to the task.
David