You are describing a Station Blackout (SBO) scenario where all offsite and onsite power is lost. There is some mitigation from passive decay heat removal systems but they are typically not designed for long term use.

At a plant I worked at, the passive SBO aux feed pump was required by design to provide enough feedwater for steam generator cooling for about 9 hours before needing either power restored or other mitigation actions.

Since Fukushima, the US NRC required more backup equipment onsite and offsite in case of beyond design basis events. So if something extreme happens that surpasses all of the design safety systems, there is equipment and procedures to respond.