I have four files:
one_file.txt
abc | def
two_file.txt
ghi | jkl
three_file.txt
m
You can loop over each file and do a check to see if the last line ends in a new line, outputting one if it doesn't.
for file in *file.txt; do cat "$file" [[ $(tail -c 1 "$file") == "" ]] || echo done > full_set.txt