It is generally assumed that there are only two ways to maintain the ends of chromosomes in yeast and mammalian nuclei: telomerase and recombination. Without telomerase and recombination, cells enter senescence, a state of permanent growth arrest. We found that the decisive role in preventing senescent budding yeast cells from dividing is played by the Exo1 nuclease. In the absence of Exo1, telomerase- and recombination-defective yeast can resume cell cycle progression, despite degradation of telomeric regions from many chromosomes. As degradation progresses toward internal chromosomal regions, a progressive decrease in viability would be expected, caused by loss of essential genes. However, this was not the case. We demonstrate that extensive degradation and loss of essential genes can be efficiently prevented through a little-studied mechanism of DNA double-strand-break repair, in which short DNA palindromes induce formation of large DNA palindromes. For the first time, we show that large palindromes form as a natural consequence of postsenescence growth and that they become essential for immortalization in the absence of telomerase activity.