Telomeres are essential features of linear genomes that are crucial for chromosome stability. Telomeric DNA is usually replenished by telomerase. Deletion of genes encoding telomerase components leads to telomere attrition with each cycle of DNA replication, eventually causing cell senescence or death. In the Saccharomyces cerevisiae strain W303, telomerase-null populations bypass senescence and, unless EXO1 is also deleted, this survival is RAD52 dependent. Unexpectedly, we found that the S. cerevisiae strain S288C could survive the removal of RAD52 and telomerase at a low frequency without additional gene deletions. These RAD52-independent survivors were propagated stably and exhibited a telomere organization typical of recombination between telomeric DNA tracts, and in diploids behaved as a multigenic trait. The polymerase-delta subunit Pol32 was dispensable for the maintenance of RAD52-independent survivors. The incidence of this rare escape was not affected by deletion of other genes necessary for RAD52-dependent survival, but correlated with initial telomere length. If W303 strains lacking telomerase and RAD52 first underwent telomere elongation, rare colonies could then bypass senescence. We suggest that longer telomeres provide a more proficient substrate for a novel telomere maintenance mechanism that does not rely on telomerase, RAD52, or POL32.