Doesn't do this for me.
echo -n abc def ghi jkl mno pqr stu vwx yza bcd efg hji; echo -n abc def ghi jkl mno pqr stu vwx yza bcd efg hji; echo abc def ghi jkl mno pqr stu vwx yza bcd efg hji
results in just simple wrapped output, with no "+". I checked my ~/.config/app-defaults/URxvt to see if I had given any special setting for this, but nothing looks relevant. And moving that aside and starting a new terminal gives me same behavior.
I do see + at the start of wrapped lines in vim. Similarly, a "@" at the end of wrapped lines in less. But I assume you're just talking about wrapped lines at the shell prompt.
Do you still see this is you temporarily move aside all your .bashrc-and-friends files and start a new terminal?