Note that in your example, Perl will keep the memory for $big_string twice:

#!/usr/bin/perl

use strict;
use warnings;
use Readonly;

Readonly my $size => 10 * 1024 ** 2; # 10 Mb.

sub show_mem {
    system "grep ^VmSize /proc/$$/status";
}

sub gimme_big {
    my $size = shift;
    my $var  = 'x' x $size;
}

show_mem;
gimme_big $size;
show_mem;

__END__
VmSize:     3464 kB
VmSize:    23952 kB
[download]

For a 10Mb string, Perl allocates about 20Mb memory.

undefing the variable makes Perl allocate about 10Mb less:

#!/usr/bin/perl

use strict;
use warnings;
use Readonly;

Readonly my $size => 10 * 1024 ** 2; # 10 Mb.

sub show_mem {
    system "grep ^VmSize /proc/$$/status";
}

sub gimme_big {
    my $size = shift;
    my $var  = 'x' x $size;
    undef $var;
}

show_mem;
gimme_big $size;
show_mem;

__END__
VmSize:     3472 kB
VmSize:    13716 kB
[download]

So, how do we get rid of the extra 10Mb? By a careful use of string eval:

#!/usr/bin/perl

use strict;
use warnings;
use Readonly;

Readonly my $size => 10 * 1024 ** 2; # 10 Mb.

sub show_mem {
    system "grep ^VmSize /proc/$$/status";
}

sub gimme_big {
    my $size = shift;
    my $var  = eval "'x' x $size";
    undef $var;
}

show_mem;
gimme_big $size;
show_mem;

__END__
VmSize:     3468 kB
VmSize:     3468 kB
[download]