I created files as follows:

./a/1234 ACS. (STUFF).txt
./b/1234 ACS. (STUFF).txt
./c/1234 ACS. (STUFF).txt
[download]

Then I ran your script with empty $top and $second = '.'. The output was:

1234 ACS. (STUFF).txt
1234 ACS. (STUFF).txt
1234 ACS. (STUFF).txt
[download]

I can't reproduce your problem.