I've got the same situation happening. Two 9 year old male cats, they only tolerate each other, one is much more aggressive. Their environment has been consistent for 5 years, only thing that changed was that a covered litter box was introduced about 3 or four months ago. Both cats have always shared the same box.
One of them, we don't know which one, is defecating behind the box, or in corners of the finished basement. Does not seem to be a urine odor smell (yet), so may only be pooping.
The vet asked if there was new stress introduced in the house, we can't think of any unless the aggressive one is becoming even more aggressive and we don't know. The vet thought that the aggressive one may be preventing the other from using the box now.
Have bought a new enclosed litter box that we will move to a bedroom upstairs where the non-aggressive cat likes to sleep. (we think that it is the non-aggressive cat who is not using the box.)
I'm taking them both to the vet in two day's time.
As this is my first post, was wondering if you cat experts have any thoughts, suggestions????
ALSO, we've used scoopable litter which is always cleaned every day.