That is because while the d option's value is required, the d option itself is not, check the definedness of $_debug afterwards:

use Getopt::Long;
my $_debug;
GetOptions('d=i' => sub {
        $_debug = $_[1];
        ($_debug > 0 && $_debug <= 4) or die "Invalid Debug Level ($_d
+ebug)"
    } ) or exit 1;

die "Debug Level is required" unless defined $_debug;
warn "Debug Level is $_debug\n";
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or set a default value before GetOptions:

use Getopt::Long;
my $_debug = 0;
GetOptions('d=i' => sub {
        $_debug = $_[1];
        ($_debug > 0 && $_debug <= 4) or die "Invalid Debug Level ($_d
+ebug)"
    } ) or exit 1;

warn "Debug Level is $_debug\n";
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