Border Enforcement, Security, And Funding Enhancement Act or the BE SAFE Act This bill requires each alien granted lawful permanent residence to pay a $2,500 fee before receiving a Permanent Resident Card (commonly referred to as the "Green Card"), in addition to any other required fees. The collected funds shall go into the newly established Border Security Enhancement Fund, and may be used to enforce immigration laws and improve immigration-related processes, including (1) constructing border barriers, (2) carrying out enforcement and removal operations, (3) improving infrastructure at border crossings, and (4) verifying the status of student visa holders.