Sorry for your loss. Most hens can tolerate low temperatures close to and below zero if they are inside a coop. It can be common to lose a hen, even off the roost during the night around the age of maturity or onset of laying. A shell-less egg is not unusual at the beginning of laying eggs, but it also can be a sign of a reproductive disorder. Where are you located? To find out what might have caused her death would be to have your state poultry vet do a necropsy. Keep the body cold in a cooler with ice, but don’t freeze it. You can sometimes tell without a home autopsy if something is obvious. Here is a list of most state vets where you can contact them early on Monday (or today if not too late
https://www.metzerfarms.com/PoultryLabs.cfm