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Nuclear envelope (NE) rupture is a hallmark of cancer cells, and persistent NE damage drives genome instability and inflammation. NE repair relies on activation of the endosomal sorting complex required for transport (ESCRT)-III repair machinery by the LEMD2-CHMP7 compartmentalization sensor, but little is known beyond these core factors. Here, we use convergent proximity proteomics to inventorise proteins mobilized to the NE upon assembly of LEMD2-CHMP7 and activation of ESCRT-III. Within this NE repairome, we identify LRRC59 as a critical regulator of LEMD2 accumulation at NE ruptures. We find that LRRC59, together with the nuclear transporters KPNB1 and XPO1, restricts the assembly of LEMD2-CHMP7 complexes to the site of rupture. Disruption of this regulatory axis escalates LEMD2-CHMP7 spreading across the NE, driving torsional DNA damage in ruptured nuclei and micronuclei. Thus, our work identifies a central regulatory layer of NE repair centered on LRRC59 and KPNB1. We propose that altered LRRC59 levels and deregulated nuclear transport coordinately compromise NE repair, driving genome instability and cancer development. Nuclear envelope (NE) rupture triggers cancer genome instability and inflammation, but mechanisms of NE repair are unclear. Here, the authors map the NE repairome and identify LRRC59 and KPNB1 as a key regulatory axis to restrain NE repair activity.