For a closed system / control mass, the mass is conserved since no mass can enter or leave the boundary of the system. So the material time derivative of mass is equal to zero.
While for an open system / control volume, mass is allowed to enter and leave the boundary of the system. The law of conservation of mass of an open system states that the material time derivative of mass within the control volume is equal to the flux of mass entering or leaving the boundary of the system.
Let us assume that we have a control volume, and after some time, a quantity of mass entered it, and no mass has left it. So in this case mass is not conserved.
So in conclusion, can we say that mass is only conserved for a closed system, while for an open system, it is conserved only if the same amount of mass that entered it,has also left it from another side? I'm confused...