Note that this only works if the thing that you're calling the -X on is an object of the overloaded class.

use warnings;
use strict;

{
    package Foo;
    use Data::Dump;
    use overload fallback=>0,
        '-X' => sub { dd @_; return 1 };
}

my $foo = bless {}, 'Foo';
print -e $foo ? 'yes' : 'no', "\n";
my $bar = "doesnotexist";
print -e $bar ? 'yes' : 'no', "\n";

__END__

(bless({}, "Foo"), "e", "")
yes
no
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