I had this exact thing happen a while back. I could not find the person in a search. I finally found her through another person's FB page who had her as a friend. I never did send the Friend request. I finally decided she must have had me blocked although she said she wanted to be "friends". I would ask her in a regular email and after a while she did not answer so I gave up and decided she did not want to be on FB with me although she said she did. I have since never heard from her again. Very strange. I never did figure any of it out. All the settings on my end were correct.