I know there are lots of instances of Vice Presidents taking over for a dead president but has the Vice President ever died as well?
We have never progressed beyond the Vice President taking over, even temporarily. The line of succession, for the top three is VP, Speaker of the House and then Secretary of State. About the closest we've come to this line of succession involved Nixon and his final fall from grace. As the Watergate scandal began to swallow up the Nixon Administration, Spiro Agnew resigned in order to plead no contest to tax evasion. This left no Vice President and would have had the Speaker of the House Carl Albert become president if Nixon was removed from office. With the confirmation of Gerald Ford, then the House Minority Leader and not otherwise on the line of succession, as Vice President, this avoided the use of the line of succession beyond the Vice President.
An interesting side note, this appointment to the Vice President's office and his loss to Jimmy Carter, Ford became the only President not elected to the Executive branch.