Well several factors have to weighed!
1. If the Vice President dies, then the 25th Amendment provision on a Vice Presidential vacancy is triggered, the President nominates a replacement & the House of Representatives votes on the confirmation of said Nominee, problem solved.
2. The president dies, the new Vice President assumes the presidency.
3. If the Vice President dies, so too does the President, the 25th doesn’t apply, the 1947 succession act comes into play, and the next in line in the succession would be the Speaker of the House, who becomes President!
4. If the Speaker has also died in a freakish act of nature , then it’s time for the President Pro Tempore of the Senate, becomes POTUS.
5. If the President Pro Tempore is dead, or is in a vegetative state (which mostly a normal situation)
, then we’ve the Secretary of State stepping up!
6. If there is a Vice Presidential vacancy & the president is unable to discharge his or her duties, or has died, before a Vice President could be nominated or confirmed, the 25th Amendment stipulates that the Speaker of the House, becomes either “Acting President” or President depending on the circumstances! The 1947 Act then comes into play again, should the new President nominates a new VPOTUS, then the normal chain of succession is re-established!
