Let's say that I am lifting an object upwards against gravity , let's say that the force which I apply is greater than the force of gravity ,so the object accelerates , now when I want to stop the object in mid air I simply decrease my force which I am applying and let the object decelerate to a stop . I know my applied force is non-conservative and hence alters the mechanical energy , however if I drop the object the energy conversion will be from mgh to kinetic energy , however my problem is when gravity did negative work during the deceleration where did the extra kinetic energy which I applied go , was it conserved or not?
Suppose that you want the object to stop then all you need to do is to no longer apply a force on the object, if you continue applying an ever decreasing force then the process described below will take longer.
The object will continue to rise and eventually stop due to the attractive force of the Earth acting on the mass.
The Earth-mass system therefore gained gravitational potential energy at the expense of the kinetic energy of the mass or you could say that for the mass alone system the gravitational force did negative work on the mass which resulted in the kinetic energy of the mass becoming zero.
Now on top of that if you did some work on the mass then all that would have happened is that the mass would have gained more height.