And after the PEB, Congress can legislate and impose a CBA on the union and its members, it happens quite often in the railroads:
At this point, the RLA has run its course. If no agreement has been reached, either side becomes free to act in its own economic interests -- a work stoppage (or strike) by labor, a lockout by management, or unilateral implementation of management proposals (that generally would force a work stoppage).
However, Congress frequently imposes its own settlement. Such congressional action is not part of the RLA. The constitutional authority for Congress to impose its own settlements is found in Article 1, Section 8 of the Constitution's commerce clause.