Bassa would almost definitely want some kind of a face-saving gesture from Willie, and that depends on how generous he is feeling, but even without anything tangible I'm sure Bassa's proven record of twisting the truth would make any agreement/climbdown look like an outright victory for Union militancy. It really is up to them to go knocking on his door.
The way I see it this is their only realistic option if they want to survive this war (sorry for yet another reference to war) in any shape or form.
Come on 'New Bassa', arise from the ashes.