It is generally accepted that cells with extensive, un-repaired DNA damage can escape cell cycle arrest only by disabling checkpoint pathways and they usually perish, after several divisions, presumably due to catastrophic events on their chromosomes. Our recently discovered PAL-mechanism opens a new perspective, that some eukaryotic cells with short chromosome ends (telomeres), usually detected as DNA damage, can escape permanent cell cycle arrest (senescence) under special conditions, despite having intact checkpoints and even immortalize, despite lacking telomerase or other telomere elongation mechanisms. Here we present the first evidence that telomerase-lacking, senescent cells generate DNA damage (single stranded DNA) at internal chromosomal regions, while the telomere proximal single stranded DNA appears to be either lost or repaired. This first evidence is from the budding yeast model system. We also discuss the possible involvement of the PAL-mechanism in carcinogenesis.