“In a chronically leaky boat, energy spent on changing vessels is more productive that energy devoted patching leaks.” – Warren Buffett
Does a project manager need to sink with his failing project if a captain is supposed go down with his ship?
It does not necessarily mean that a captain must go down with his ship. It is intended to indicate that the captain is ultimately responsible for his ship and his passengers.
You are the project manager and have ultimate responsibility for your ship, your passengers, and your crew. Your ship is your project and the objectives that you are supposed to achieve, while your passengers are your team members or other stakeholders. Sometimes, your ship or project is not viable or suitable for the sea. It is up to you to distinguish between abandoning the project too soon and holding on past the point of no return. It is a waste of time and money to keep a failing project going for too long. You are wasting time and money if you keep the failing project going. It can also be demoralizing for you and your team.
You have done everything you can to get your team to achieve your project objectives. Do not abandon the ship. Get a new ship! Transfer your passengers to a larger, more seaworthy vessel first.
Find a way of changing ships. Change jobs is not necessarily what I mean. However, it is possible. As I said, lead your stakeholders to understand what is and isn’t possible. Reassess their goals. If they don’t have any goals, help them define specific objectives that can be achieved. This will allow you to change your ship.
It is more productive than trying to rescue a failing project as it leaks more and sinks deeper into the abyss.
Do not go down with the ship, buy a new one!

Go down with the ship?