my $dollar1;
case /^\s*(\S+)$ (?{ $dollar1 = $1 })/ {
   ...

##</code><code>##

use strict;
use warnings;

sub do_re {
   my ($re, $var) = @_;
   
   $var =~ /$re/;
   print("inside: $1\n");
}

{
   my $re = qr/(b)/;
   print("$re\n");

   do_re($re, 'abc');
   if (defined($1)) {
      print("outside: $1\n");
   } else {
      print("outside: [undef]\n");
   }
}

print("\n");

{
   my $dollar1;
   my $re = qr/(e)(?{ $dollar1 = $1 })/;
   print("$re\n");

   do_re($re, 'def');
   if (defined($dollar1)) {
      print("outside: $dollar1\n");
   } else {
      print("outside: [undef]\n");
   }
}

__END__
(?-xism:(b))
inside: b
outside: [undef]

(?-xism:(e)(?{ $dollar1 = $1 }))
inside: e
outside: e