use File::Basename;

my @files = reverse <DATA>;
my $found;
foreach ( @files ) {
  chomp;
  next unless basename($_) =~ m/^(\d+)$/;
  $found = $1;
  last;
}

die "No matches found.\n" unless defined $found;
print $found;

__DATA__
/path/to/one/library
/path/to/another
/path/to/another/01
/path/to/another/s
/path/to/another/02
/path/to/another/w1
/path/to/another/03
/path/to/another/1e
/path/to/another/2014