In the case of XML::Parser it has its own __DIE__ handler which makes things a little tricky. But this is perl, the language where "never" doesn't really mean "never", it just means "probably shouldn't" ...

BEGIN {
  ## Use CORE::die if you still want exceptions
  *CORE::GLOBAL::die = sub {
    warn "Problem? What problem? ... [@_]\n";
  };
}

use XML::Parser;

XML::Parser->new->parse("This isn't XML. Seriously");
print "All is well\n";

__output__

Problem? What problem? [
syntax error at line 1, column 0, byte 0 at /usr/lib/perl5/XML/Parser.
+pm line 187
]
All is well
[download]