Is it possible for me to allow it to catch some of the standard signals, such as HUP?

Sure. You use the special %SIG hash. Read all about it in perlipc.

Here's a quick demo:

$ perl -le '$SIG{ HUP } = sub { print "Bye cruel world."; exit }; slee
+p 60' &
[download]

Just kill -HUP the resulting process before the minute is up...

-sauoq
"My two cents aren't worth a dime.";