Tested and verified. Apparently, the sections stay static, and if the string becomes shorter, the length of the string, plus one or two characters, overwrite the $<digit> variables. If you regexp again, though, they get reset as they should be. What I tried:

use re 'debug';
use strict;
my (@rere,$rere);
$_="hello world";
@rere = /(\w+)\s+(\w+)/;
$rere = "(".join(",",@rere).")";
print "\$1 = $1, \$2 = $2, \$rere = $rere\n";
$_="foo bar";
print "\$1 = $1, \$2 = $2, \$rere = $rere\n";
@rere = /(\w+)\s+(\w+)/;
$rere = "(".join(",",@rere).")";
print "\$1 = $1, \$2 = $2, \$rere = $rere\n";
[download]

with the following output:

Compiling REx `(\w+)\s+(\w+)'
size 15 first at 4
   1: OPEN1(3)
   3:   PLUS(5)
   4:     ALNUM(0)
   5: CLOSE1(7)
   7: PLUS(9)
   8:   SPACE(0)
   9: OPEN2(11)
  11:   PLUS(13)
  12:     ALNUM(0)
  13: CLOSE2(15)
  15: END(0)
stclass `ALNUM' plus minlen 3
Compiling REx `(\w+)\s+(\w+)'
size 15 first at 4
   1: OPEN1(3)
   3:   PLUS(5)
   4:     ALNUM(0)
   5: CLOSE1(7)
   7: PLUS(9)
   8:   SPACE(0)
   9: OPEN2(11)
  11:   PLUS(13)
  12:     ALNUM(0)
  13: CLOSE2(15)
  15: END(0)
stclass `ALNUM' plus minlen 3
Matching REx `(\w+)\s+(\w+)' against `hello world'
[...]
Match successful!
$1 = hello, $2 = world, $rere = (hello,world)
$1 = foo b, $2 = r rld, $rere = (hello,world)
Matching REx `(\w+)\s+(\w+)' against `foo bar'
[...]
Match successful!
$1 = foo, $2 = bar, $rere = (foo,bar)
Freeing REx: `(\w+)\s+(\w+)'
Freeing REx: `(\w+)\s+(\w+)'
[download]

As for the null character, that might be a byproduct of C(++) string processing -- for those who may not know, in C(++) strings are terminated with a null.