If you can fit all the lines and actually want to process them as separate lines then you can use a negative lookahead assertion to split just on linebreaks that aren't followed by plus signs:

{
  local $/;
  foreach (split /\n(?!\+)/, <>)
  {
    s/\n\+/ /g;
    print "$_\n";
  }
}
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Then you just have to substitute out the internal linebreaks and pluses that are left. (You may not want the space in there depending on your data.)

Note that as a side-effect, the split has chomped the input, so a \n may be needed in the output.