I am a retired federal employee who was involved in the federal budget process. Even after receiving their annual appropriations from Congress, federal departments and agencies always have the option to request a supplemental appropriation, usually (but not always) for previously unanticipated needs.
In this light, Congress could now approve appropriations for the 8-9 Federal departments (including DHS), the shutdown would end, and then DHS could make a request to Congress, for a supplemental appropriation related to border security. This request would then be subject to congressional review and then a straight up-and-down vote would occur in both the House and Senate, if Senate Majority Leader Mitch McConnell let such a vote occur in the Senate. This is the way our democracy is supposed to function. – Jim Witeck Apex