Perhaps the people of the Buddha's day weren't as haunted about nihilism as we in the West are today. In paticcasamuppáda isn't death more or less lumped in with aging and "this entire mass of suffering"? The source of our dukkha is our holding our experience in subjection, appropriating it as mine, be it in dying or simply eating food.
From Letter 37
What, precisely, is upādāna (grasping, or as I prefer, holding) if it is not synonymous with cetanā (intention)? This, and not any other, is the fundamental question raised by the Buddha's Teaching; and it is extremely difficult to see the answer (though it can be stated without difficulty). The answer is, essentially, that all notions of subjectivity, of the existence of a subject (to whom objects are present), all notions of 'I' and 'mine', are upādāna. Can there, then, be intentional conscious action—such as eating food—without the notion 'It is I who am acting, who am eating this food'? The answer is, Yes. The arahat intentionally eats food, but the eating is quite unaccompanied by any thought of a subject who is eating the food. For all non-arahats such thoughts (in varying degrees, of course) do arise. The arahat remains an individual (i.e. distinct from other individuals) but is no longer a person (i.e. a somebody, a self, a subject). This is not—as you might perhaps be tempted to think—a distinction without a difference. It is a genuine distinction, a very difficult distinction, but a distinction that must be made.
[37.1] a difficult distinction: As his letters to the Ven. Ñānamoli Thera make clear, this distinction was the Ven. Ñānavīra Thera's last major insight prior to his attainment of sotāpatti. Although certainly this particular perception need not be pivotal for all who achieve the Path, that it was so for him is one reason for the strong emphasis the author lays on this point in the Notes as well as in various letters.
There is of course a profound difference in an Arahant's "passing away" and a puthujjana's "dying", but the same profundity is true for any experience.