It looks to me like asking Word to open the document is failing, here:

my $doc = $word->{'Documents'}->Open("$file") or next; #TODO: log 
+error
[download]

The debug output pretty much stops after that. I can't explain why it still prints Done with connection, though, unless the code you're actually running is slightly different than what you posted.

I would add that error logging mentioned in the TODO, and also some error checking after you close statements (at least on Unix, some errors aren't reported until the file is closed).