Providing subsidies affects Marginal Private cost but not Marginal Social Cost?
The amount of external cost is determined by the level of production in this framework. 

If the producers receive a subsidy the MPC shift to the right as you point out. That also means that for each level of cost production increases and therefore the external benefits are less, that is, they are internalizised. If the subsidy is enough the external benefits of production are zero and the MPC=MSC.