If I understand you correctly, you want to allow mass flowing out of the system (model domain) and prohibit mass entering the system. If this is true, you can use a fixed mass Boundary Condition (type Dirichlet) on top of a flow Boundary Condition. Then, you may constraint the mass Boundary Condition with a minimum mass flow of 0 g/d as you already indicated. In this configuration, the Boundary Condition for mass is only active as long as water is entering the system. If water leaves the system, mass is transported out by the advective mass transport component (convective formulation of the transport equation).