Metastatic cancer cells traverse constricted spaces that exert forces on their nucleus and the genomic contents within. Cancerous tumors are highly heterogeneous and not all cells within them can achieve such a feat. Here, we investigated what initial genome architecture characteristics favor the constricted migratory ability of cancer cells and which arise only after passage through multiple constrictions. We identified a cell surface protein (ITGB4) whose expression correlates with increased initial constricted migration ability in human melanoma A375 cells. Sorting out this subpopulation allowed us to identify cellular and nuclear features that pre-exist and favor migration, as well as alterations that only appear after cells have passed through constrictions. We identified specific genomic regions that experienced altered genome spatial compartment profiles only after constricted migration. Our study reveals 3D genome structure contributions to both selection and induction mechanisms of cell fate change during cancer metastasis.