Which type of fusion occurs in a high-mass star near the end stages of its life cycle?

The answer is "iron fusion".

In fact, initially all stars burn hydrogen through nuclear fusion. As they run out of hydrogen, they start to burn the next heavier element, which is helium. The very massive stars continue this cycle, and when they run out of helium they start to burn the heavier elements until reaching iron. This element represents the end of the chain, because nuclear fusion of iron does not release energy, but it absorbs energy. This means that the star can't produce energy anymore and eventually it collapses.