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?
TERM
set toTERM=rxvt-unicode
? What window manager are you using - gnome? i know xmonad has acrlf off
option specifically related to copying from the terminal, but not sure if this is what's driving your problem or if there is a related fix in whatever WM you're using.