One more variant:

#!/usr/bin/perl

# https://perlmonks.org/?node_id=11106665

use strict;
use warnings;
use Data::Dumper;
$Data::Dumper::Indent = 0;

my $string_three = "a aa 21a a 123 a b9 b bb aa1 1aa aa11 11aa [b42] (
+12a)";

my @captures = $string_three =~ m{
    \b ([ab])? (\d+) ([ab])? \b
    (?(?{ 1 != grep defined, $1, $3 }) (*FAIL) )
    }xmsg;

print "RESULTS: ", ( Dumper \@captures ), "\n";
[download]

RESULTS: $VAR1 = [undef,'21','a','b','9',undef,'b','42',undef,undef,'1
+2','a'];
[download]

It generates triplets with one undefined value ($1 or $3), but you can grep defined values as AnomalousMonk mensioned.

EDIT:
Sorry for mistake. I changed condition "2 == grep defined, $1, $3" to "1 != grep defined, $1, $3", because one of $1 or $3 must be defined.

ADDED:

my @captures = $string_three =~ m{
    \b ([ab])? (\d+)
    (?(1) | ([ab]) ) \b
    }xmsg;
[download]

Similar approach using conditional. It captures in same way.

ADDED-2:
Also:

my @captures = $string_three =~ m{
    \b ([ab])? (\d+) (?(1) (*ACCEPT) ) ([ab]) \b
    }xmsg;
[download]