You are reaching the limit of my understanding. Specifically, if you execute the script:

#!/usr/bin/perl
use strict;
use warnings;
use 5.012;

use Phases;

my $main_closure = bless {name => 'main_closure'}, 'Phases';
sub closure {
    say $main_closure;
}
my $external = bless {name => 'external'}, 'Phases';
END       { say 'Main END'     }
say 'Main Last line';
[download]

with the module

package Phases;
use 5.012;

BEGIN     { say 'Phases BEGIN' }
UNITCHECK { say 'Phases UNITCHECK' }
CHECK     { say 'Phases CHECK' }
INIT      { say 'Phases INIT'  }
END       { say 'Phases END'   }

my $my = bless {name => 'my'}, __PACKAGE__;
my $closure = bless {name => 'closure'}, __PACKAGE__;
our $our = bless {name => 'our'}, __PACKAGE__;

sub closure {
    print $closure;
}
sub DESTROY {
    my $self = shift or say 'Nothing passed to DESTROY' and return;
    my $name = $self->{name} || '<undef>';
    say "Phases DESTROY $name"
}

1;
[download]

(borrowed heavily from Know the phases of a Perl program’s execution) outputs

Phases BEGIN
Phases UNITCHECK
Phases DESTROY my
Phases CHECK
Phases INIT
Main Last line
Phases DESTROY external
Main END
Phases END
Phases DESTROY closure
Phases DESTROY our
Phases DESTROY main_closure
[download]

What I hear you saying is that you problem happens between "Last line" and "Main END". Are there any variables scoped at script level going out of scope? If you have suspects, you can stick them into closures to make them persist longer; that might identify which package's destructor is responsible.