Actually, the problem is how we understand the term "people". Most often, we believe that a people is a kind of primordial given that appears in ancient times and maintains its integrity for centuries, despite the circumstances. The people necessarily have attributes: language, cultural traditions, habitat, history, etc. Moreover, in our minds a people is synonymous with a nation, which is a political sovereign and is capable of creating a state. Within the framework of such a mental construction, it is really very difficult to imagine that a people could suddenly disappear.
But imagine that a people is just a certain group of people who rally for some economic reason or for military purposes. Usually a people is a phase of the development of a tribal family, but there are often cases when the substrate is ethnically, linguistically and culturally heterogeneous (for example, the Khazars). If his cohesion turns out to be successful, that is, the intended goals are realized, then after several generations this group becomes relatively homogeneous through marriages and intra-group communications. If the rallying is unsuccessful, the group disintegrates.
Another way of the appearance of the people is through military male unions, which, occupying a dominant position in some area, begin to marry local women (Goths, Franks, Romans). An analogue of the male union is colonization, which, as a rule, is also carried out by men. As an example, one can name the Bukhtarma masons, who are mainly (but not only) immigrants from the Arkhangelsk province, and who, having moved to the Irtysh, actively intermarried with local women of Turkic or Mongolian origin.
The stage of appearance. people are always elusive, like the stage of extinction. For example, we cannot say exactly when the Krivichi appeared, and also when exactly they disappeared. Of course, “disappeared” does not mean physical disappearance, but the rejection of self-identification “Krivich”. Physically, the descendants of the Krivichi (at least some of them) remained on the land of their ancestors, but the ethnonym "Krivichi" ceased to be used by them.
In the future, some Krivichi began to call themselves Pskovites, others - Smolensk, still others - Polotsk. Moreover, this change in different groups occurred at different times. At the same time, they mixed with the neighboring peoples - the Ugrians, Balts, Scandinavians. Then, from these mixes, other peoples appeared, and on their basis, nations. As a result, the Krivichi served as a substrate for Russians, Belarusians, partly Lithuanians.
Dispersed and assimilated, decreasing in numbers below the "observed limit". They ceased to "name themselves" and generate cultural objects associated with this people.