In reply to gethin_allen:
> So if this detergent can do this to a stainless steel spoon god knows what it can do to a nylon rope.
Maybe you didn't lose the plastic cup, maybe the washing powder has eaten it! :-O
No, of course it hasn't. The cardboard box is doing fine too no doubt. Your argument is somewhat fallacious. Nylon is not stainless steel, and contrary to what many may think stainless steel is not immune from corrosion. (Some grades more so than others.)
The OP's rope is probably fine, and he's probably going to be wanting to replace it anyway because 'probably' is probably not good enough.