I'm not up on the legal fine points of this issue (IANAL), but it seems that the following is true.
Bankruptcy. Debts that are discharged in bankruptcy do not generate COD income. This is, AFAIK, an explicit provision in the tax code. Although I am not really conversant with bankruptcy law, as a layman I would think that a debt not asserted to the bankruptcy court would be discharged and not just those that were asserted.
Probate. Here things are perhaps a bit fuzzier. What I don't know is if there is any provision similar to that regarding discharge of debt in a bankruptcy. But, on the other hand, if we think about the purpose of probate and why debt gets barred, it seems to me that it is so that the final financial affairs of the decedent can be wrapped up. Given that goal, it seems odd (OK, not a good legal argument) that after the close of probate, things can happen which will cause claims on the probate estate.
Presumably when probate closes, the estate can be distributed. So what assets are then even available for paying taxes on any COD income that arises because of the statutory bar to collecting the debt? Are the heirs on the hook? The executor of the estate? Or is this a case where the estate, at the time the COD arises is considered insolvent (it no longer has any assets), and that the COD income is not taxed based on insolvency?