That's exactly what makes it a closure.

Lexical variables live in their own symbol tables (that's not what they're called in Perl 5, but it's the concept: just a mapping of a name to the data structure that represents the appropriate variable container). They nest — that's why you can write code like this:

my $foo = 'outside';

{
    my $foo = 'inside';
    print "Inside: '$foo'\n";
}

print "Ouside: '$foo'\n";
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If you dump the optree with something like B::Concise, you'll see enter, leave, and pad operations. The enter and leave ops govern which symbol table (scratch pad or lexical pad, in Perl 5 terms) is active. Think of it like a stack and you'll get it. The pad operations look up a symbol in the scratch pad.

Subroutines (anonymous and named) are represented by data structures called CVs (basically, Code Values). Every CV is attached to a lexical symbol table. That's just a place to store the lexical variables declared and used within that subroutine.

To handle the nesting issue, there has to be a way to look outward from inner scopes. If there's no $foo in the tightest, most innermost scope, look outward, one scope at a time, to find the nearest appropriate $foo. (This is complicated a little bit by global variables, which are handled with a different symbol table implementation in Perl 5. There also appears to be variable analysis because of the pad ops, not glob ops. Insert handwaving here; I really don't want to read that code right now.)

The code example you're asking about is a closure so that nested variable scopes will work. Or, put the way it actually happened, because nested variable scopes had to work, closures were possible.

use strict;      
use warnings;    
                 
my $foo = 'foo'; 
bar();           
                 
$foo = 'bar';    
bar();           
                 
sub bar {        
  print "$foo\n";
}
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sub foo1234 {    
                 
use strict;      
use warnings;    
                 
my $foo = 'foo'; 
bar();           
                 
$foo = 'bar';    
bar();           
                 
sub bar {        
  print "$foo\n";
}                
}                
# Execute once
foo1234();
# Execute twice
foo1234();

OUTPUT:
foo
bar
bar
bar
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