The program is changed to:

#!/usr/bin/perl

use strict;
use warnings;
use TestFor;

my @e; // moved outside as suggested before
tie @e, 'TestFor', 0;

my $i = 0;
BIGLOOP: while (1) {
#       my @e;

        for  my $j (0..@e / 2 - 1) {
                print "died where I shouldn't have: $i\n";
                last BIGLOOP;
        }
        $i++;
}
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The file TestFor.pm:

package TestFor;

use Carp;

sub TIEARRAY {
    my $class    = shift;
    my $elemsize = shift;
    if ( @_ || $elemsize =~ /\D/ ) {
        croak "usage: tie ARRAY, '" . __PACKAGE__ . "', elem_size";
    }
    print "TIEARRAY\n";
    return bless {
        ELEMSIZE => $elemsize,
        ARRAY    => [],
    }, $class;
}

sub FETCH {
    my $self  = shift;
    my $index = shift;
    print "FETCH\n";
    return $self->{ARRAY}->[$index];
}

sub STORE {
    my $self = shift;
    my ( $index, $value ) = @_;
    if ( length $value > $self->{ELEMSIZE} ) {
        croak "length of $value is greater than $self->{ELEMSIZE}";
    }

    # fill in the blanks
    $self->EXTEND($index) if $index > $self->FETCHSIZE();

    # right justify to keep element size for smaller elements
    $self->{ARRAY}->[$index] = sprintf "%$self->{ELEMSIZE}s", $value;
    print "STORE\n";
}

sub FETCHSIZE {
    my $self = shift;

    #print "FETCHSIZE\n"; // was called very often
    return scalar @{ $self->{ARRAY} };
}

sub STORESIZE {
    my $self  = shift;
    my $count = shift;
    if ( $count > $self->FETCHSIZE() ) {
        foreach ( $count - $self->FETCHSIZE() .. $count ) {
            $self->STORE( $_, '' );
        }
    }
    elsif ( $count < $self->FETCHSIZE() ) {
        foreach ( 0 .. $self->FETCHSIZE() - $count - 2 ) {
            $self->POP();
        }
    }
    print "STORESIZE\n";
}

sub DESTROY {
    print "DESTROY\n";
}

1;
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