Breckinridge served the Confederacy in various capacities, and was briefly thought to have been killed in action in late 1863. "Speak no ill of the dead" was not, in this case, the policy of the New York Times:
"If it be true, as is now positively declared, that a loyal bullet has sent this traitor to eternity, every loyal heart will feel satisfaction and will not scruple to express it. Ordinarily, enmity is disarmed before death; reproach is silenced, and even the sternest justice makes way for pity. The form that is shrouded is a sacred thing, and the grave itself is an altar on which every bitter feeling should be sacrificed forever. Human censorship does not presume to follow the spirit that has gone to its Eternal Judge; and even the most rigid feels constrained to remember his own frailties, and forgive. But where Death strikes such a public enemy as this, it exacts no silent obeisance. Personal feeling has no part in the matter. It is to be regarded purely as a public event; and if it really has the shape of a public deliverance, it is just as right to welcome it as any other public blessing. It is just as proper, too, to speak the truth of such a criminal when dead as when living. Humanity has a just reckoning with guilt of this particular dye that can never be satisfied without posthumous infamy."
After the fall of the CSA, the former vice president spent a few years in exile but returned to Kentucky after President Johnson's Christmas Day amnesty in 1868. He practiced law and was a railroad executive in the years remaining to him.
Oddly, if the scant information available on line is to be believed, one of the vice president's grandsons and his namesake was John Cabell "Bunny" Breckinridge -- who is best remembered for his part in Plan 9 From Outer Space.