It depends on if there is an external force acting on the object or not.
If there is no other force, the drag force will reduce the velocity to zero- it is stopped!
If there is a constant force, the drag force will only make the object reach a terminal valocity.
i.e. F[sub]total[/sub]= F[sub]ext[/sub] -av[sup]b[/sup] then av[sup]b[/sup]=F[sub]ext[/sub]
so terminal velocity v[sub]t[/sub]=e [sup]log(Fext/a)/b[/sup]