perl -we "sub fail{die 'test'}; END{ print qq'\nF\n'; fail() }; 
$SIG{__DIE__} = sub{print qq!\nS\n!; fail()}; fail()"

S
test at -e line 1.

F

S

S
test at -e line 1.
[download]

I like line numbers, so I wrote this up as little program:

#!perl -w
use strict;
my $counter = 0;
sub fail{ ++$counter; print "$counter: Fail called.\n"; die "DEATH ". 
+__LINE__ ."\n" } 
END{ ++$counter; print "$counter: End called.\n"; fail() }
$SIG{__DIE__} = sub{ ++$counter; print "$counter: SigDie called.\n"; f
+ail() }; 
fail()
[download]

1: Fail called.
2: SigDie called.
3: Fail called.
DEATH 4
4: End called.
5: Fail called.
6: SigDie called.
7: Fail called.
8: SigDie called.
9: Fail called.
DEATH 4
[download]

Not exactly, as an END block gets always executed. Even if your script dies a present END block will be executed.
cite from perlman:perlmod

An END subroutine is executed as late as possible, that is, after perl has finished running the program and just before the interpreter is being exited, even if it is exiting as a result of a die() function. (But not if it's polymorphing into another program via exec, or being blown out of the water by a signal--you have to trap that yourself (if you can).) You may have multiple END blocks within a file--they will execute in reverse order of definition; that is: last in, first out (LIFO). END blocks are not executed when you run perl with the -c switch, or if compilation fails.


Have a nice day
All decision is left to your taste

Sure, it's an endless loop. It's just that infinity's pretty short for a dead program.