Based on the below, it doesn’t seem unreasonable to understand death as something we are always inescapably liable to:
Bhikkhus, there are these five themes that should often be reflected upon by a woman or a man, by a householder or one gone forth. What five? (1) A woman or a man, a householder or one gone forth, should often reflect thus: ‘I am subject to old age; I am not exempt from old age.’ (2) A woman or a man, a householder or one gone forth, should often reflect thus: ‘I am subject to illness; I am not exempt from illness.’ (3) A woman or a man, a householder or one gone forth, should often reflect thus: ‘I am subject to death; I am not exempt from death.’ (4) A woman or a man, a householder or one gone forth, should often reflect thus: ‘I must be parted and separated from everyone and everything dear and agreeable to me.’ (5) A woman or a man, a householder or one gone forth, should often reflect thus: ‘I am the owner of my kamma, the heir of my kamma; I have kamma as my origin, kamma as my relative, kamma as my resort; I will be the heir of whatever kamma, good or bad, that I do.’ -AN 5.57
Couple with:
There are, bhikkhus, these three kinds of intoxication. What three? Intoxication with youth, intoxication with health, and intoxication with life. (1) An uninstructed worldling, intoxicated with youth, engages in misconduct by body, speech, and mind. With the breakup of the body, after death, he is reborn in the plane of misery, in a bad destination, in the lower world, in hell. (2) An uninstructed worldling, intoxicated with health, engages in misconduct by body, speech, and mind. With the breakup of the body, after death, he is reborn in the plane of misery, in a bad destination, in the lower world, in hell. (3) An uninstructed worldling, intoxicated with life, engages in misconduct by body, speech, and mind. With the breakup of the body, after death, he is reborn in the plane of misery, in a bad destination, in the lower world, in hell. -AN 3.39
…it looks to be the careless intoxication that impedes the ability to understand the full scope of what we are subject to in this life. Based on my understanding of the Serbian Ajahn Nyanamoli and Ven. Nanavira, this is the immediacy of death that they are describing: an intoxication with life, understood to be mine, still includes an inherent liability to death, and this must be thoroughly contemplated to undermine the intoxication. Previously in AN 3.39:
Again, it occurred to me: ‘An uninstructed worldling, though himself subject to death, not exempt from death, feels repelled, humiliated, and disgusted when he sees another who has died, overlooking his own situation. Now I too am subject to death and am not exempt from death. Such being the case, if I were to feel repelled, humiliated, and disgusted when seeing another who has died, that would not be proper for me.’ When I reflected thus, my intoxication with life was completely abandoned.
Otherwise, the individual remains liable to both, i.e., birth and death remain as aspects of the experience; of samsara; of the “origin of this mass of suffering.” This is the obvious difference from the linear understanding of other models of DO, where birth and death are understood as events to be experienced, and as such, future lives are the liability. I do not believe Ajahn Nyanamoli would take issue with seeing the next life as liability in this way, but would likely stress that it endures presenty here and now, which is none other than how death (and likely destination) is described above in AN 3.39.
From that point of view, this is what the two models have in common, however, in terms of samsara, there are always innumerable births to consider; eons and eons of births that were once a mere liability, but became an actuality because of a lack of understanding the four noble truths - not to mention the potential for innumerable future births if the problem is not solved now. The three lives model doesn’t disregard this by any means, but both Vens Nanavira and Nyanamoli understand DO as applying to a much broader and more immediate situation, and prefer to avoid a scheme that would limit the extent to which any of the factors can be presently discerned and felt.
It should be noted, however, that this doesn’t alter what the twelve factors are defined as individually, but introduces significant depth to roles of each in the origin of the mass of suffering. This seems to be one of the most often misunderstood points.
As an aside…I don’t recall anything specific, but this was likely discussed at various points in the lengthy correspondence between the British Ven. Nanamoli and Ven. Nanavira.