In yeast telomerase mutants, the Sgs1 RecQ helicase slows the rate of senescence and also facilitates the appearance of certain types of survivors of critical telomere shortening via mechanisms dependent on Rad52-dependent homologous recombination (HR). Here we describe a third function for Sgs1 in telomerase-deficient cells, inhibition of survivors that grow independent of Rad52. Unlike tlc1 rad52 double mutants, which do not form survivors of telomere dysfunction, tlc1 rad52 sgs1 triple mutants readily generated survivors. After emerging from growth crisis, the triple mutants progressively lost telomeric and subtelomeric sequences, yet grew for more than 1 year. Analysis of cloned chromosome termini and of copy number changes of loci genome-wide using tiling arrays revealed terminal deletions extending up to 57 kb, as well as changes in Ty retrotransposon copy numbers. Amplification of the remaining terminal sequences generated large palindromes at some chromosome termini. Sgs1 helicase activity but not checkpoint function was essential for inhibiting the appearance of the survivors, and the continued absence of Sgs1 was required for the growth of the established survivors. Thus, in addition to facilitating the maintenance of telomere repeat sequences via HR-dependent mechanisms, a RecQ helicase can prevent the adoption of HR-independent mechanisms that stabilize chromosome termini without the use of natural telomere sequences. This provides a novel mechanism by which RecQ helicases may help maintain genome integrity and thus prevent age-related diseases and cancer.