Como dizer "beco sem saída" em inglês

Matheux,

- have your back (to/against) the wall

Exemplos:

He owes money to everyone - he's really got his back to the wall now.
Ele deve para todo mundo. Ele está em um beco sem saída.

I refer to him as the man with the golden hands. Matthew was in Yves care when he was critically ill and this man saved his life. He had his back against the wall. He even said to us, "I have my back against the wall," but he goes, "I'm not giving up". - Google.au

Post relacionado. (Uma vez lá, dê um CTRL + F por "beco sem saída").
Catch-22 (beco sem saída)

Cul-de-sac = ponto além do qual avanço ou progresso parecem impossíveis.

"his own investigations into the substantiality of matter lead him into a cul-de-sac — Leslie Paul"
(Suas investigações quanto à substancialidade da matéria levaram-no a um beco sem saída -- Leslie Paul)

Literally I´d translate the phrase of Matheux like this, is it correct?

Mr. So-and-so is now going out with that Such a one, and he´s in a blind alley, his life is being destroyed/ruinned.

Jlmmelo,

"Blind alley" não é usado desta forma, por isso, não considero seu uso neste contexto adequado.

Para o significado literal de beco sem saída - rua sem saída - sugiro "dead end" ou "dead-end street.''

Definitions:

If a street is a dead end, there is no way out at one end of it. [Collins]
Dead end: a street that ends instead of joining with another street so that there is only one way in and out of it. [Merriam-Webster]

Exemplo de uso:

• We came to a dead end and had to turn around. [Nós chegamos a um beco sem saída e tivemos que voltar.]

Dica adicional: dead end costuma ser utilizado como verbo, significando chegar a um beco sem saída.

• You will dead end at Holander and then take a right. [Você vai chegar a um beco sem saída na Holander, e então vire à direita.]

Bons estudos.