Why is my battery appear to be at 0% when it can still be charged?

In the middle of the day my battery went from 50% to 0% in an instant but still retained some charge. Phone will not charge above 0%, but will still have some power to use. After a certain amount of time the phone will go black and cannot be turned on again until a long charging session is used. There is no warning beforehand and it turns off unexpectedly, no matter the length of the charging session.