Answer
Yes — build a Custom Event on the TRANSACTION_SYS_LOCAL event/table, which tracks background job transaction state, with an Event Action that emails both the IT/support team and the specific user who generated the error whenever a background job transaction lands in a Warning or Error state. This both helps stop the same user from repeatedly triggering the same recoverable error unnoticed, since they're now directly notified and can take follow-up action, and surfaces genuinely larger systemic problems to the support team for proper investigation.