A null (zero) character will confuse PHP's password_* functions, when using bcrypt encryption (which is the default), so it's probably safe to just refuse any password with this character.

To illustrate:

$dangerous_pwd = 'foo' . chr(0) . 'bar';
$wrong_login_1 = 'baz';
$wrong_login_2 = 'foo';

$hash = password_hash($dangerous_pwd, PASSWORD_DEFAULT);

if (password_verify($dangerous_pwd, $hash))
  echo "this is good!\n";

if (password_verify($wrong_login_1, $hash))
  echo "this shouldn't happen! (1)\n";

if (password_verify($wrong_login_2, $hash))
  echo "this shouldn't happen, but does! (2)\n";
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