Telomeres are an unusual component of the genome because they do not encode genes, but their structure and cellular maintenance machinery (which we define as "telotype") are essential for chromosome stability. Cells can switch between different phenotypic states. One such example is when they switch from maintenance mediated by telomerase (TERT telotype) to one of the two alternative mechanisms of telomere preservation (ALT I and ALT II telotype). The nature of this switch is largely unknown. Reintroduction of telomerase into ALT II, but not ALT I, yeast led to the loss of their ability to survive a second round of telomerase withdrawal. Mating-based genetic analysis of ALT I and II revealed that both types of telomerase-independent telomere maintenance are inherited as a non-Mendelian trait dominant over senescence (SEN telotype). Additionally, inheritance of ALT I and ALT II did not depend on either the mitochondrial genome or a prion-based mechanism. Type I, but not type II, survivor cells exhibited impaired gene silencing, potentially connecting the switch to the ALT telotype epigenetic changes. These data provide evidence that nonprion epigenetic-like mechanisms confer flexibility on cells as a population to adjust to the life-threatening situation of telomerase loss, allowing cells to switch from TERT to ALT telotypes that can sustain viable populations.