Xemnas and Xigbar have been allies before they were even turned into nobodies. In fact, Braig had worked for Master Xehanort before he even possessed Terra. After he did possess Terra, Braig immediately recognized him and realized that he was faking his amnesia. The two continued to work as apprenticed of Ansem the Wise while secretly conspiring a plan together. They eventually gave themselves to the darkness and became nobodies named Xemnas and Xigbar. Together they helped found Organization XIII as numbers I and II respectively.
Xemnas and Xigbar continued to work closely while they were in Organization XIII. Xigbar helped recruit Marluxia into the organization per Xemnas' request. He also eavesdropped on Xemnas when he went into the Chamber of Repose. Xigbar was eventually destroyed and reappeared as Braig in Radiant Garden. He immediately left and joined the true Organization XIII which Xemnas is a member of. Sora confronted Braig on the fact that he is going to become another person to which he responds that he is already halfway to becoming Xehanort.
XemXig is a fairly popular Kingdom Hearts ship though it does not seem to be as popular as many other organization ships including XemSai. However, it still does have its fans. This was mainly after Kingdom Hearts: Birth by Sleep when it was revealed that Xemnas and Xigbar had been quite close on their plans before Organization XIII was even formed. Popularity increased even further in Kingdom Hearts 3D: Dream Drop Distance when it was revealed that Xigbar was willing to become a vessel for Xehanort.
- Xigbar seems to have known about Xehanort's true plan before even joining Organization XIII and does not seem to mind becoming a vessel for him.