A dead president is § 1 of the 25th Amendment to the U.S. Constitution.
As people including Brian C. Kalt have noted, a missing president (which covers one who is missing and that people assume to be dead, albeit who is not legally declared dead) is § 4 of the 25th Amendment.
A president who is missing is fairly obviously "unable to discharge the powers and duties of his office", whether or not xe is actually dead.
A president who was missing and is no longer so, and where the vice-president took over under § 4, goes through the procedure given in that section to regain the presidency, transmitting a notice that the inability does not exist, and gets to be the president again unless the vice president successfully contests it and wins the necessary supermajority in Congress.
The controversial applications of § 4 that people foresee are where it is used for political ends.
A president who has gone missing, through accident, kidnap, capture, or some other means, is not really that sort of controversial situation; and indeed Congressional discussions of the original amendment when it was enacted, later in the 1970s, and even earlier in the 1930s and 1890s (which talk about the president being captured or kidnapped) all clearly indicate that a sudden event that renders the president incommunicado, or paralysed, or not locatable, or inaccessible, or in general unequivocally physically unable to perform the job and unable to even communicate that inability (which would rather be § 3 of the amendment), is the aim of the section.
It's not about death.
It's about whether there is a lack of a person able to do the job, in the view of the person who would take over.
That person takes over temporarily, unless the president is unable even to successfully challenge that, with the system being intentionally weighted in the president's favour.