Is it possible for half of an outlet to not work?

Yes, it is entirely possible for only half of a duplex wall outlet to work while the other half remains completely dead, a malfunction typically caused by a broken internal contact tab or a split-circuit wiring configuration. In many residential kitchens, bathrooms, and dining areas, duplex outlets are wired as split-circuits where the small brass break-off tab connecting the top and bottom hot terminal screws is intentionally removed so each half can be controlled independently by separate switches or circuits. Alternatively, physical wear can break an internal spring contact inside one half. You can troubleshoot split-circuit wiring safely by isolating power at the circuit breaker. You can verify that your corrective action is successful when removing the wall plate, inspecting the brass tab, and replacing a damaged receptacle restores full power to both plug slots.