* Remain at rest if it was initially at rest. This is due to Newton's First Law of Motion, also known as the Law of Inertia. An object at rest will stay at rest unless acted upon by a net force.
* Continue moving at a constant velocity if it was already in motion. This is also a consequence of Newton's First Law. An object in motion will stay in motion at a constant velocity (same speed and direction) unless acted upon by a net force.
In other words, a zero net force means there's no change in the object's motion. It will either stay still or continue moving at a constant speed in a straight line.