First off you've declared the sub as having no arguments. Secondly within the curly braces of the sub you have changed context and $i is uninitialized within that context and therefor you are going to print zeros for each iteration.

Here is code that does what you think it should:

foreach (0, 1) {
    my $i = $_;
    sub my_print {
        my $i = shift;
        print $i;
    }

    my_print( $i);
}
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Now... you could have saved yourself a lot of pain if you had

use strict;
use warnings;
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