Short-read sequencing is the workhorse of cancer genomics yet is thought to miss many structural variants (SVs), particularly large chromosomal alterations. To characterize missing SVs in short-read whole genomes, we analyzed 'loose ends'-local violations of mass balance between adjacent DNA segments. In the landscape of loose ends across 1,330 high-purity cancer whole genomes, most large (>10-kb) clonal SVs were fully resolved by short reads in the 87% of the human genome where copy number could be reliably measured. Some loose ends represent neotelomeres, which we propose as a hallmark of the alternative lengthening of telomeres phenotype. These pan-cancer findings were confirmed by long-molecule profiles of 38 breast cancer and melanoma cases. Our results indicate that aberrant homologous recombination is unlikely to drive the majority of large cancer SVs. Furthermore, analysis of mass balance in short-read whole genome data provides a surprisingly complete picture of cancer chromosomal structure.