There's no interpolation involved. The sub contains a lookup of a variable's content, so the variable needs to remain unchange if you want the output of the lookup to be constant.

You can do this by copying the value of $str into into a variable that doesn't change, and using that variable instead.

sub make_closure {
   my ($str) = @_;
   return sub { $str };
}

my $str = 'hi';
my $sub = make_closure($str);

say $sub->();   # 'hi'
$str = 'hello';
say $sub->();   # 'hi'
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You could actually interpolate the current value into code, but producing code is trickier.

my $str = 'hi';
my $sub = eval qq{ sub { "\Q$str\E" } } or die $@;

say $sub->();   # 'hi'
$str = 'hello';
say $sub->();   # 'hi'
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