Telomeres ensure genome integrity and are maintained by telomerase. During replicative senescence, telomerase is inactivated, telomere sequences progressively shorten, and set the limit for cell proliferation. As telomeres shorten, they are thought to lose their protective caps at a critical short length, activating the DNA damage response and recruiting DNA damage repair activities that would degrade, fuse, or recombine dysfunctional telomeres. However, the structure(s) of short and dysfunctional telomeres, which respectively trigger permanent replicative senescence or potentially promote genome instability, remain unclear. To define the structure of telomeres at the point of dysfunction and the fate of cells carrying them, we developed a system called FinalCut to induce a single telomere of defined length in cells in which we can conditionally inactivate telomerase. This allows structural analysis of this telomere, and combined with the use of our microfluidic system to track consecutive cell cycles from telomerase inactivation to cell death, we can achieve single telomere and single cell resolution. Our results show that the loss of telomere stability is progressive as the telomere shortens, and that telomeres of a given length can be protected or unprotected in separate cells. We conclude that telomere length is not the sole determinant of the switch between functional and dysfunctional telomeres. We therefore propose that the minimum length of telomeres to maintain cell viability follows a probabilistic, rather than deterministic, model.