Anyone with a passing familiarity with US politics knows what happens in the event of the death of the President: the Vice President takes over, and next in line after the VP are several other people as established in the 25th Amendment. But what if the VP dies instead? Are there established procedures for replacing him/her?
A replacement is nominated and voted on based on the 25th Amendment.
Amendment XXV Section 2
Whenever there is a vacancy in the office of the Vice President, the President shall nominate a Vice President who shall take office upon confirmation by a majority vote of both Houses of Congress.