Nuclear atypia, including altered nuclear size, contour, and chromatin organization, is ubiquitous in cancer cells. Atypical primary nuclei and micronuclei can rupture during interphase; however, the frequency, causes, and consequences of nuclear rupture are unknown in most cancers. We demonstrate that nuclear envelope rupture is surprisingly common in many human cancers, particularly glioblastoma. Using highly-multiplexed 2D and super-resolution 3D-imaging of glioblastoma tissues and patient-derived xenografts and cells, we link primary nuclear rupture with reduced lamin A/C and micronuclear rupture with reduced lamin B1. Moreover, ruptured glioblastoma cells activate cGAS-STING-signaling involved in innate immunity. We observe that local patterning of cell states influences tumor spatial organization and is linked to both lamin expression and rupture frequency, with neural-progenitor-cell-like states exhibiting the lowest lamin A/C levels and greatest susceptibility to primary nuclear rupture. Our study reveals that nuclear instability is a core feature of cancer, and links nuclear integrity, cell state, and immune signaling.