I explained in a previous post that it's actually pretty unlikely that your DNA results will show a match with a given relative as close as fourth cousins. On the other end of the spectrum is that even though it's unlikely, you could match a small number of very distant relations. Here's an example I've come across recently.
I was looking for my recent DNA matches and I found someone that Family Tree DNA suggested was a fourth to distant cousin. This means we match a very small amount of DNA. Looking at his list of surnames, I saw a few that looked very familiar to me. They were surnames found among my great-grandfather, Aloys Panther's ancestors in and around Moesbach, Ortenaukreis, Baden, Germany.
I sent this match an email and I provided a family tree showing Aloys' ancestors. I asked if any of the names looked familiar. In the end, we discovered that we shared two pairs of ancestors, Adam and Magdalena Klumpp and Martin Baudendistel and Magdalena Steimers. Martin is my 7x-great-grandfather and Adam is my 8x-great-grandfather. This is eight and nine generations distant.
What are the odds I'd match this person that is so distantly related? The odds are very slim that I'd match any given individual. However, given the number of descendants of any ancestor this long ago, it's pretty likely I'll match another descendant of theirs. Of course, the odds narrow considerably when looking for any one of the descendants that had their DNA tested with Family Tree DNA.
I tend to believe our odds of showing as each others' matches are improved due to endogamy. This means that our relatives in this group of small villages have been intermarrying for so long they're all distantly related and share a larger portion of DNA than you would normally expect.