They have thick roots on Pandora, being one of the first settlers to arrive on Pandora. They operate a pub which also acts as their base of operations just outside the town of Overlook. However they have always been at odds with another well known clan, the Hodunks.
The Zafords as a clan appear in Borderlands 2 at odds with the Hodunks. For this they are willing to hire any mercenary to attack the other clan. This leads to the Clan War quests. While the entire clan as a whole appears only in Borderlands 2, a member appears in Borderlands. Lucky Zaford who is Mick Zaford's son runs a bar called Lucky's Last Chance Watering Hole in the Dahl Headlands is a part of the clan.
A Zaford clan member appears in the intro for Tales from the Borderlands unearthing a loot box, he is then assassinated by a generic bandit wielding the Skullmasher.