TextSoap is not doing this. Given that Living Writer is a web app, it is more likely they changed the paste behavior in a recent update.
MacOS does have a feature called "Smart CopyPaste" (Edit > Substitutions > Smart CopyPaste) which will insert spaces if needed when enabled.
It works pretty well in Safari for web apps that use standard text fields, but I don't know if the other browsers mimic the behavior or not or if custom fields break it.
The test you can do to verify it is not TextSoap is to use TextEdit. Copy and paste text in TextEdit and look at its behavior with and without Smart CopyPaste enabled.
Once you understand where it happening, you can look at some options to address it.
For example, assuming it is Living Writer, you can create a cleaner that removes any space from the end of the text found.
I'm using the \x{20} to be explicit, but you can also just put a space or \s (which also matches a tab at the end) if you wish.
Make sure to change the options to be: s so $ works on the entire text, not just lines.
Once you create the cleaner, you can then add it to the end of any cleaner you need.