Some antinuclear antibodies (ANAs) bind extracellular nucleic acids released into tumor environments and are pulled into the nuclei of live cancer cells through nucleoside salvage pathways, independent of tumor-specific surface antigens. Here we show that ANA nuclear penetration induces nuclear flux by the lysosomal protease cathepsin B and leverage this mechanism to design an antinuclear antibody-drug conjugate (ANADC) with cathepsin B-labile drug linker. The ANADC targets nucleic acid exhaust from necrotic tumors and crosses membrane barriers through nucleoside salvage as a DNA-seeking and tumor agnostic antinuclear missile cancer therapy.