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. When telomeres shorten, they are thought to lose their protective caps at a critical short length, which activates the DNA damage response and recruits 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 have developed in Saccharomyces cerevisiae 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 cells reach senescence earlier and more synchronously, as the shortest telomere is set at a shorter length. This is in agreement with the first telomere reaching a short length being sufficient to trigger senescence in budding yeast. Below a certain threshold, the shorter telomere becomes unstable and degrades. However, we can define a length for which a short telomere appears to be stable, and the cells stop dividing at the same time. Combined with a mathematical model of senescence, our results suggest that the probability of a telomere signaling senescence increases as it shortens, but at low frequencies. When a telomere reaches a critical length, it can be stably maintained in cells, while activating the DNA damage checkpoint, without causing obvious fusions or degradation. The structure of this critically short telomere will be discussed.