The PMBoK is a body of knowledge guide. It is not even THE body of knowledge. It is not a methodology and it will not "tell" you what to do. You will, however, find the basis of information you are looking for in the PMBOK in Integration, Cost Management, Stakeholder Management, and Risk Management. It talks about funding, securing funding from stakeholders, monitoring the funds, reporting on the variances, capturing those variances in your risk management, using contingencies, and of course closing the project. You will have to connect the dots because, again, the PMBOK is not designed to do that.
To answer comment: I cannot speak for how PMI collectively would answer your question but I can provide what I would do in your situation. First, there is a dependency on the type of contract you have. If a firm fixed price type, the lack of funding is irrelevant assuming they funded you and are paying you the fixed price agreement and assuming there is no scope creep. If those two assumptions are true, you continue working until you have provided your scope per your contract.
If T&M or Cost Plus, as the PM I would have made known the funding risk as early in the project as possible, i.e., when I knew it, and begin the process of asking for more funds. If the ask was rejected, I would--again, as early as possible--start recommendations on descoping the project in order to fit what remains. If the customer refused to even consider this, I would inform them of the date funds run out and when my team stops work. On that date, I would stop the work, invoice whatever remains in terms of what they owe me, perform other contract close out activities, and then start my next gig.