My cat was doing this about a year ago - urinating & defecating at the end of the hall. After taking him to the vet, treating him for an infection, and doing all of what I'm about to say below, he stopped the behavior.
Only the vet can tell for sure if there is a physical reason for this behavior change. UTI's & other infections are common & it is best to rule them out by a visit to the vet. Other things to do to: Limit where the cat can go. Keep it out of the bedrooms & areas where it can do things without you seeing. Isolate in a laundry room or bathroom when you are not home or at night when you are asleep. Put a bell on the cat's collar so you can hear when it is headed for forbidden areas. Keep the litter box super clean all the time. Do you have more than 1 cat? This one may have decided it doesn't want to use the same box as others. It may take weeks before you figure out & correct the problem. Hope something here helps. Good luck.