What does the Pali canon say about "death"? I'm just clinging to this notion that the small death (of prthagjanas) is never reversible, and never incomplete.

Leaving aside the notion of "karma" and "rebirth" and "continuity", what does the Pali canon say about "death"?
“Paticca Samuppada” is a discourse on the process of birth and death. As per the scriptures, a being is a stream of Mind connected ‘ Nama-Rupa’. When a person dies, no soul departs. The stream of consciousness ( viññana) upon death, becomes one of the contributing causes for the arising of a new set of five aggregates of clinging (Panca Upadana Khandas)  elsewhere.  In the Attakara sutta, you will find that you do exist. But there is no permanent self in you and the five clinging aggregates (panca upadanakkanda) which constitutes you is beyond your control, and therefore Anatta (non-self). (read  Anatta Lakkana Sutta).

The understanding of death &amp;  impermanence is an antidote to desire and ill-will, is an encouragement to our practice of Dhamma, and is a key to understanding the ultimate nature of things, the way things really are.
Remembering death especially is said to be like a friend and a teacher to one, as it acts as a discouragement to excessive desire and ill-will. While death itself is certain, the time of death is uncertain. We can die at any moment. Life is like a candle in the wind, or a bubble of water. At any moment it may be snuffed out. At any moment it may burst. Thus, we ought to practice the Dhamma quickly so that we may not waste this opportunity and this precious human life.

The Buddha once gave a discourse on the impermanence of life at the village named ‘Alavi’. He admonished, 'Practice meditation on death. Reflect mindfully: Uncertain is my life, certain is my death, certainly one day I have to face death.'

The Buddha also exhorted his listeners to be always mindful and to strive to perceive the true nature of life. He also said, 'As one who is armed with a stick or spear is prepared to meet an enemy and some other poisonous and dangerous animals, so also, one who is ever mindful of death should face death mindfully. He will then leave this world for a good destination. – “Blind is this world. Few are those who clearly see. As few birds escape from a net, few go to a blissful state.” '

In many a suttas it is shown that beings in the un-ending Samsara (cycle of birth-and-death) are bound to eye as ‘me’ (considering eye as ‘me’). In a similar manner, beings are bound to ear as ‘me’, nose as ‘me’, tongue as ‘me’, body as ‘me’, and mind as ‘me’.

As long as they are bound to all these faculties, they are actually bound to Māra. In order for one to free from this bond of Māra, one needs to investigate the notion of ‘me’ about each faculty (eye, ear, nose, tongue, body, and mind) separately.

We should see that there is nothing permanent in rūpa (figure), vēdanā (feeling), saññā (perception), sanskāra (intention; volitional effort), and Viññāna (consciousness). But, we are bound to these five groups of clinging because of the thought of ‘me’. That binding results in a birth. That binding results in our death. That binding results in getting another life (birth) after our deaths.