As it's a problem with two constraints, I assume that x3 and x4 are slack variables. Going back a step, I recreate the original problem as
-x1 + x2 <= 1
x1 - 2x2 <= 2
x1 - x2 is to be minimised with x1, x2 non-negative
As the objective function is parallel to the first constraint boundary, multiple solutions exist, being anywhere along that boundary "northeast" of (0,1), so in general the solution is x1 >= 0, x2 = x1 + 1, o.f. = -1
The original problem has an unbounded feasible region, which is why there is only one optimal BFS, i.e vertex. If another constraint is added to truncate this, e.g. x1 + x2 <= 3, another optimal BFS will be found after the first iteration has exchanged x2 and x3. In the case suggested, this will exchange x1 and x5 (the new slack variable) to give a second optimal BFS at (1,2). The complete solution will then be any point between this and the original one at (0,1).