The short answer is that you should not use the \b anchors in this case; just remove them from your regex.

Here is a more Perl-ish way to code this up:

use strict;
use warnings;

my @array1 = qw(
    abc_RCF_BM_allocation_0_kl     
    aplc_RCF_BM_allocation_0_in_nml
    fbe_RCF_BM_allocation_0_in_tvg 
    ap_hu_BM_allocation_0_in_nml
);

my @array2 = qw(
    RCF_BM_allocation_0_in
    BM_allocation_0
    RCF_BM_allocation_0
);

for my $i (0 .. $#array1){ 
    for my $j (0 .. $#array2){ 
        if ($array1[$i] =~ /$array2[$j]/) {
            print "$array1[$i] contains $array2[$j]\n";
            last;
        }
    }
}

__END__
abc_RCF_BM_allocation_0_kl contains BM_allocation_0
aplc_RCF_BM_allocation_0_in_nml contains RCF_BM_allocation_0_in
fbe_RCF_BM_allocation_0_in_tvg contains RCF_BM_allocation_0_in
ap_hu_BM_allocation_0_in_nml contains BM_allocation_0
[download]