You have a lapsed beneficiary of a pension plan, presumable ERISA qualified.
The options in an ERISA qualified plan are: (i) there would be an Order of precedence in the Plan documents that will award the decedent's share to his wife, children, parents, siblings, estate, etc; or, (ii) the beneficiary designation form will condition receipt of his share by saying "if he survives the settlor, and if he doesn't survive the settlor, then the decedent's share passes to the other members of the class to which he was a member, that is the other two children in this case; or, (iii) the share of the deceased beneficiary reverts back to the Plan.
In my experience, absolute silence on the subject is rare.
If the annuity is ERISA qualified, and if ERISA does not address the situation, or if the annuity is not ERISA qualified, then state law will apply (and state law will not/cannot be preempted by ERISA).
See my attached Memo re: terminable interests.
But see Boggs v. Boggs - at https://supreme.justia.com/cases/federal/us/520/833/#tab-opinion-1960143
where the Supreme Court held that ERISA preempts state community-property law allowing a non-participant spouse to transfer by a testamentary instrument an interest in undistributed pension plan benefits. That would seem to strip the deceased party in the CuseFan example, and his heirs and next of kin would have no claim to the lapsed 1/3rd share, and the deceased party's share would pass to the other two children.
Buy on the other hand we have FERS and OPM and 5 CFR 838.237(b)(3) and the attached Memo demonstrating how another Federal Law deals with this situation.
And here is how TSP handles a deceased beneficiary - https://www.tsp.gov/for-beneficiaries/determining-beneficiaries/ Not the comment: "A will, prenuptial agreement, separation agreement, property settlement agreement, or court order will not override either a beneficiary designation or the order of precedence."
At the end of the day it is difficult to understand how the Plan passed muster without addressing this matter.
David
TERMINABLE INTEREST DEFINED BENEFIT PLANS REV'D 03-16-24.pdf
OWNERSHIP INTEREST 5 CFR 838.237(b)(3).pdf