for both of these object
system1: earth and ball
if a ball is falling down, is the work done on it positive since force and displacement are in the same direction.
system 2: earth and basket
a basket is tied to a rope and is dropped then come to a full stop, then is the work done also positive as well
System 1: Yes, work is done by the gravitational field. Work done is the same as the loss of potential energy.
System 2: Work is done while it falls, but when it stops, all that work (which became kinetic energy) is converted to heat.