Stationary players can be guilty of fouls. Last season I called one on a big kid in the middle of the floor, and he was dumbfounded because he'd been stock still for about 4 seconds before the dribbler tripped over his foot.
Of course, his feet were about 6 feet apart at the time...
(And, to the wiseass who asks me whether his shoulders were 6 feet wide, the answer is "no."
)