A couple of obvious ones:-

'Sam Hall'

Up the ladder I did grope,
that's no joke, that's no joke
Up the ladder I did grope, that's no joke.
Up the ladder I did grope,
and the hangman spread the rope,
O but never a word said I,
coming down, coming down,
O never a word said I coming down.

'Polly on the Shore'

And here I lie a-bleeding on the deck
And for her sweet sake must die.
So farewell to me parents and me friends,
Farewell my dear Polly too.
I'd ne'er would have crossed this salt sea so wide
If I had have been ruled by you.

The jilted sailor in Cyril Tawney's 'Sally Free and Easy' may not be at the point of death but he is not far off.....

Think I'll wait till sunset,
See the ensign down,
Then I'll take the tideway,
To my burying ground,

Sally, free and easy,
That should be her name,
When my body's landed,
Hope she dies of shame.