Bhava-chakra, the wheel of life, or, as I would translate it, "the wheel of individuation" is a relatively late depiction of the 12 Nidanas. In the suttas of Pali Canon, the nidanas are usually presented as a list, that is reviewed both in forward as well as in reverse direction -- but never (to my knowledge!) as an infinite loop.
If you read the wheel clock-wise, the 12 nidanas are:
avidya -> samskara -> vijnana -> nama-rupa -> six ayatana -> phassa -> vedana -> tanha -> upadana -> bhava -> jati -> jaramarana & dukkha
Although the interpretation of the wheel as depicting the cycle of death-and-rebirth is accepted by most schools, according to Triyana framework it represents the basic/literal ("hinayana") level of understanding.
Instead, some instructors, including Chogyam Trungpa Rinpoche, taught twelve nidanas as a process of gradual individuation, or emerging and hardening of the illusory ego.
In this line of thinking,
avidya is the innate ignorance,
samskaras are the arbitrary imprints of sensory stimulation,
vijnana is inductive intelligence born from the imprints,
nama-rupa are inductively postulated external objects, six
ayatanas are the implied "windows" onto the world,
phassa is a subjective experience of contact with the postulated objects,
vedana is a sensation attributed to the contact,
tanha is an obsessive replay of the contact and sensation,
upadana is feeding the obsession by making its object one's goal,
bhava is becoming the "this" of here-and-now, dependently-co-arisen with the twofold "that" of space-and-time,
jati is identifying with a living organism, and
jaramarana is experiencing the organism's perspective culminating in death.
(Because the list shows subjective experience, not an objective physical process, the physical birth is not shown, but if it were, it would fit right before Ignorance. The Birth that is shown, is not a physical birth, but conceptual (subjective) assumption that one is an individual living organism.)
Although 12 nidanas explained this way describe subjective experience of one sentient being, which begins with physical birth and ends with death, we could say that after death the cycle logically "restarts" from scratch, again starting from ignorance, progressing through individuation, and culminating in death of another "being" and so forth indefinitely.
To be sure, objectively there is no cycle, beings arise and cease asynchronously, but in some sense we could say that death of a (unenlightened) being is a return to innate ignorance.
@ChrisW found a tremendously elegant quote in Wikipedia:
When the cessation of the continuity of experience occurs, we speak of death. It is the total breakdown and dissolution of experience and experiencer. The process of disintegration, destructuring, and entropic scattering yields a nexus of vibratory murkiness which is the condition of avidyā, the first motif. Thus the entire structure of patterning feeds back on itself.