Good question Nelson,
There are some but I have no idea of what is their name. As I was advised commercial growing centers around having fig varieties that are pollinated because the fig crops will be of a larger size. There are probably also crops that do not require pollination but are pollinated...
One interesting variety Artona Karpit or Partona Karpit ( I am unsure of the exact spelling) that has no requirement for pollination on the breba crop but the second crop requires pollination. This certainly an interesting case and I should probably check with my sources for the exact spelling. When I visited the Erbeyli fig research institute they had a few specimens.