Break-induced replication (BIR) is a mechanism to repair double-strand breaks (DSBs) that possess only a single end that can find homology in the genome. This situation can result from the collapse of replication forks or telomere erosion. BIR frequently produces various genetic instabilities including mutations, loss of heterozygosity, deletions, duplications, and template switching that can result in copy-number variations (CNVs). An important type of genomic rearrangement specifically linked to BIR is half-crossovers (HCs), which result from fusions between parts of recombining chromosomes. Because HC formation produces a fused molecule as well as a broken chromosome fragment, these events could be highly destabilizing. Here we demonstrate that HC formation results from the interruption of BIR caused by a damaged template, defective replisome or premature onset of mitosis. Additionally, we document that checkpoint failure promotes channeling of BIR into half-crossover-initiated instability cascades (HCC) that resemble cycles of non-reciprocal translocations (NRTs) previously described in human tumors. We postulate that HCs represent a potent source of genetic destabilization with significant consequences that mimic those observed in human diseases, including cancer.