The range operator leads to a fairly clean solution:

use strict;
use warnings;

my @subs = (
    ['AAAAAA', 'f11', 'f12', 'f13', 'BBBBBB'],
    ['CCCCCC', 'f21', 'f22', 'DDDDDD'],
);

while (my $line = <DATA>) {
    if (@subs) {
        my $state = $line =~ /^$subs[0][0]$/ .. $line =~ /^$subs[0][-1
+]$/;
        
        if (($state) =~ /E0$/) {
            print join "\n", @{$subs[0]}, '';
            shift @subs;
        }

        next if $state;
    }

    print $line;
}

__DATA__
aaa
aaa
AAAAAA
ccc
ddd
BBBBBB
111
222
333
CCCCCC
444
555
666
DDDDDD
777
888
999
[download]

Prints:

aaa
aaa
AAAAAA
f11
f12
f13
BBBBBB
111
222
333
CCCCCC
f21
f22
DDDDDD
777
888
999
[download]

If you don't want the marker lines in the output use:

            print join "\n", @{$subs[0]}[1 .. $#{$subs[0]} - 1], '';
[download]

for the print line.