It would be great to see how the program died.
Usually there is a stack trace on stderr.

Currently supervisord restarts task and I'm getting email
Process xxx in group xxx exited unexpectedly (pid 416525) from state RUNNING

which is not useful, then I login and ask for current output but it's long ovewritten by new instance.

So it would be great to include tails into email (like 20lines each), we shouldn't get many emails in the first place, but when we do it should contain very useful info.