Bellman Ford Source & Negative Cycles
The source distance does not need to be treated specially. It can change like any other vertex. In this scenario, it'll be updated to -1 by the end of the fourth round. The weights into and out of B will never become quiescent: either B's distance will be more than 2 greater than G's distance, or (say) A's distance will be more than 5 greater than B's distance. So the cycle will still be detected.
Now, if you ever find yourself reducing the source distance below zero, you immediately know that there's a negative cost cycle, and can terminate early. But there's no need to do so for the algorithm to work.