There is a book called Good Cats,Bad Habits-the Complete A to Z Guide
for When Your Cat Misbehaves written by Alice Rhea ( a judge for the
Intenational Cat Association(TICA) and the editor of TICA Trend, a
magazine. She's been a cat trainer for ten years). The whole book is on
the possible cause, prevention and correction of a whole host of problems
concerning felines.Under" Defecating Far From the Litter Box " she says "
when cats urinate or defecate in an unusual place, it's a signal that
something is out of whack in their world. Defecating at a distance from
the litter box indicates there may be a disturbance in its vicinity . ...
try to determine whether anything changed in the house to cause it. Has
the litter box been moved to an unacceptable location( it ) needs to be
moved to a relatively quiet spot away from the heavy traffic
pattern....cats will try hard to confine their elimination to the litter
box but if they can't get to it in a reasonable time they will take the
next available spot .. an inquisitive dog, a rambunctious child or an
adult who walks too fast or too heavily pst the litter box may may her
feel the the box is not in a safe place...like people , cats like a little
privacy and peace and quiet when they are using the toilet.... do not
scold or punish her - she is not doing it because she wants to but because
something is wrong. ....cats are naturally fastidious creatures. given
their choice they will always use a clean litter box that is placed in a
quiet convenient location . Place the litter box in quiet , low-traffic
areas where there is some privacy for the cat. Make sure that the location
is such that she cant accidentally ber closed out of the room where her
box is located. Train children and dogs to respect the cat's right to
privacy."
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One woman tried this. She used a covered kitty litter box and put it in a
quiet, low-traffic area easily accessible by the cat. As of right then, no
more problem. And this cat had been defecating on the furniture for three
months . Why? the stress of two moves the last move to a small apartment
where everything was crowded, including the pets, plus various emotional
upsets  in the household.