SQL 2012 :: Capture Deleting Job Details?

One of our Application creating run time SQL job to run batch process and application itself deleting this run time SQL job, but when doing deletion it’s not checking whether job is running or not, just doing direct delete. Our challenge is how to capture deleted job details, after incident happen we could see error details only in this log.

We can run profile to trace but we don’t know when it will trigger and we cannot possible keep active profiler as it will kill server.so we can't run the trace for log time as we don't know when the issue happens.