Making America Safe and Secure Act of 2019 or the MASS Act This bill authorizes grants for states to implement or maintain firearms and firearms dealer licensing requirements. A state's requirements must incorporate certain elements, including the following: an individual must have a firearms license at the time of acquiring, and during the entire period of possessing, a firearm or ammunition; and an individual who sells, rents, or leases a minimum number of firearms, or sells ammunition, must obtain a firearms dealer license.