This reminds me of someone who was unfaithful or flakey, but they are sorry and don't want the other person to leave.
They are saying even when there are problems, they'll stay and won't go back to their old ways.
I think the lines:
"Even when the ship is wrecked, I promise
Tie me to the rotten deck, I promise"
are saying that even if the relationship is damaged beyond repair, they'll stay and "go down with the ship", in a sense.
This reminds me of someone who was unfaithful or flakey, but they are sorry and don't want the other person to leave. They are saying even when there are problems, they'll stay and won't go back to their old ways. I think the lines: "Even when the ship is wrecked, I promise Tie me to the rotten deck, I promise" are saying that even if the relationship is damaged beyond repair, they'll stay and "go down with the ship", in a sense.