Old age leads to degradation in hunting skills. As a result, looking for easy prey like village cattle and animals. Villagers retaliate and lead to the tiger's death. If easy prey is not so easy to get, starvation sets in.
Another reason is younger ones making a claim for their territory. Fighting with younger tigers can lead to injuries, broken canines. If the canines of a Tiger or any other Cat are lost, the life expectancy is reduced drastically. If the injuries are deep, it leads to a fatal outcome.
Many tigers die of territorial fights in their older age than starvation. Each tiger has its area or beat … as the tiger gets older, a younger one generally takes over the territory and a fight ensues between the original tiger and the new one. But yes there have been cases of tigers dying out of starvation.