I still wonder why is $& always null in the original example.

... why is $& always null in the original example.

I think the answer is that $ (in the original example) and \z (in the example below) match after the last character in the string: that's the 'position' of the end of the string. For instance, in the string 'xa' the 'a' can match and is replaced, but after this match the match position (as returned by pos) is just beyond the end of the string, where it can match once again with no 'a', no whitespace and \z — a zero-length match!

>perl -wMstrict -le
"my @strings = ('x', 'xa', 'x ', 'xa ',);
 ;;
 for my $s (@strings) {
   $s =~ s{ a? \s* \z }
          { print qq{\$& '$&'  pos = }, pos($s);  ''; }xmseg;
   print qq{\$s '$s' \n};
   }
"
$& ''  pos = 1
$s 'x'

$& 'a'  pos = 1
$& ''  pos = 2
$s 'x'

$& ' '  pos = 1
$& ''  pos = 2
$s 'x'

$& 'a '  pos = 1
$& ''  pos = 3
$s 'x'
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Update: N.B.: The /g regex modifier does not act to 'reset' $&, $1, or other match variables.