§ 48 Death or Incapacity of Offeror or OffereeAn offeree’s power of acceptance is terminated when the offeree or offeror dies or is deprived of legal capacity to enter into the proposed contract.
However, both barbi and CALI discuss how irrevocable offers (e.g. options) don’t terminate in this situation. I decided to look up the caselaw. It’s likely that most jurisdictions track to California on this issue.
“An option is an offer and if it is without consideration, it is revoked by the death of the offeror prior to acceptance. *452 If consideration is given, it is a contract binding upon the offeror and upon his successors in interest after his death. See case cited in 6 Cal.Jur., pp. 48–53, §§ 27, 28, 29; Williston, Contracts (Revised Ed.), §§ 61, 62; Cal.Civ.Code, § 1587(4).” (Bard v. Kent (1942) 19 Cal.2d 449, 451–452 [122 P.2d 8, 10])
So an irrevocable offer does not terminate by operation of law in the case of death or incapacity. A successor in interest can be the decedent’s estate, etc.