Someone close to me was a double orphan. I don't know the full details, but I believe that him/her and their two siblings were all abandoned by their mother, and put into an orphanage. The father may have been different for them, there's no way to know unless we found and asked the mother. Two of them, the ones I know, we're adopted from Russia to America in 1999. The third one is still in Russia probably, there's no real way to know after 20 years.

So yes, somebody having no parents or biological relatives as a child is incredibly rare. Luckily the people that adopted them have been great parents, and you'd never know they were adopted from Russia unless they told you.