Does this basket ball rule exist?

During play, can one player be left alone in the other court (their offensive court), that lone player waiting for an outlet p from a rebound or inbound? Can you just leave him in his offensive court side indefinitely? Is their a rule preventing this? I've seen so many players doing this in street games but not in pro basketball... Well, taking out one man is a disadvantage, but having one man waiting in the other side will let you score quicker and easier...