I guess it depends on what has gone wrong. With cronjobs you can set an email address where the output of the cronjob goes to. So whenever a script runs and output is generated, this will be emailed to the given email address.
If something just dies and no output is generated, there is no way of knowing this. In that case you would need some sort of script that verifies the cronjob finished successfully.
The cronjob is working, that I know because I get an email as well with the export as .CSV. That is for me the sign the export did his job.
But in the same export, there must be transferred this .CSV to an SFTP-server. And this is not always working. When I see the logs in CSVImproved, the latest error was: no connection possible.
So, what I see is that CSVImproved does know when it isn't finished the way it should. It would be helpfull if in that case there is an email alert or something.
We are using the export to get webhop orders shipped by an shipment company. When export fails, orders can't be sent.