If you purchase a new DRL socket for your 2003 Cadillac Escalade. it should come with "pigtail" wires attached to the socket. Those wires can then be soldered or crimp connect to the vehicle wiring harness after the damaged socket has been cut off.
RepairPal Certified shops can diagnose and repair your 2003 Cadillac Escalade EXT. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.