This is why you should write full-coverage testsuites — in the course of testing every path, you are likely to find edge cases that you had not recognized before.

For this particular problem, the easiest solution, assuming that you chomp each input line is to put the code that adds before and after strings in an unless (m/^$/) block. (If you do not chomp the input, change the regex match to m[^$/$], quickly tested here with perl -e 'while (<>) { print "empty\n" if m[^$/$] }' and typing some sample input.)