Or perhaps more properly, any $SIG{__DIE__} handler you install should only ever be used to augment the exception and re-throw it. Anything else completely breaks perl's exception handling mechanism. Here's a working (and useful) example of a good $SIG{__DIE__} handler:

local $SIG{__DIE__} = sub {
  my $err = shift;
  if (ref($err)) {
    die $err;
  }
  else {
    throw Exception::Unknown (error => $err);
  }
};
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Implementation of the Exception::Unknown class is left as an exercise. Also note the use of local - so that if we're running under something like mod_perl we don't screw up everyone elses handler that might not want this effect.