According to the docs $^S may be set inside the die() handler even if you're not inside an eval. So that's why it appears that $SIG{__DIE__} has been reset. If you put a print statement before the die() you'll see that $^S is set within the $SIG{__DIE__} handler.

# slightly revised die() handler

sub die_handler {
    # added this line
    print "\$^S is set to $^S", $/;
    die @_ if $^S;

    print "ERROR: $_[0]\n (Check logs for more info)\n-----\n\n";

    exit(1);
}

__output__

Warn before init! at die_code.pl line 3.
WARNING: Warned at die_code.pl line 7.

 (Check logs for more info)
-----

$^S is set to 1
Caught: died inside eval!

$^S is set to 1
Died for real! at die_code.pl line 28.
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HTH

broquaint