An alternative is provided for each equipment on board. 

If Emergency fire pump is damaged or not working, one of the fire and GS pump can be given emergency power supply and it will act as an emergency pump.

In case emergency generator is not working, we still have three generators (AE).

If one lifeboat has some issues, we still have another lifeboat and/or Liferafts on board.

But who decides if these alternative arrangements are enough for the vessel to be called a "seaworthy ship"?

The answer is Flag state of the ship.

If any of the safety equipment is not working, the ship manager needs to notify the flag state and classification society of the vessel.

Classification society will advise the alternate arrangements. Once these alternative arrangements are in place, flag state may issue a dispensation for certain period.

Once this dispensation is received, the ship can sail to the high seas.

Even with this dispensation, ship manager and master must ensure that this fact is made known to the ship's charterers and any other party affected by the ship operation.

I will share similar situation on one of the ships I was sailing as Master.

Main engine governor developed an issue and the main engine could only be maneuvered from the emergency station in the engine room.

The vessel was arriving a US port and we informed the class, Flag, and USCG for this defect. USCG. USCG allowed the ship to berth with one extra escort tug.

Class surveyor boarded the vessel and issued a Condition of class and allowed the ship to sail to next port as the spares and technician were available and arranged for that.

The vessel was carrying the oil major cargo and we informed the oil major too. Even though flag, class, and USCG allowed the ship to sail, oil major insisted that ship cannot even move to the anchorage area and must not leave the berth without rectifying the issue.

There was some delay but the technician and the spares were brought to this port next day and vessel only moved after rectifying the issue.

So it is not only the Flag and the class of the ship but also the charterers that we must inform about this significant defect. 

In the case of an issue with any safety equipment, Machinery or bridge equipment, the ship must not sail without a flag dispensation on board.