Glossary entry (derived from question below)
Portuguese term or phrase:
perdido por um, perdido por mil
English translation:
nothing to lose, everything to gain
Portuguese term
United States
BA in Transl., MA in ESL, 15 yrs of exp.
Native in: Portuguese 
Works in: English to Portuguese, Portuguese to English, Spanish to Portuguese, and 2 more.
perdido por um, perdido por mil
Em um jogo normal, as equipes temem atacar porque se arriscam a sofrer um contra-ataque. No caso de uma equipe já estar perdendo, essa preocupação não se justifica, pois tanto faz perder de 1x0, 2x0, 3x0 ou 1000x0 (mil a zero) dá no mesmo.
Generalizando, essa expressão é usada quando não se tem mais nada a perder, quando uma pessoa está em uma situação difícil e só tem uma saída, que é arriscada. Assim, se essa alternativa única não funcionar, na pior das hipóteses ela ficaria na mesma, ou seja, mal." (WordReference)
I wonder if there's an English idiom for this. I found this explanation in English:
"... having started something, see it through to its end, rather than stopping short thereof: perdido por cem, perdido por mil; perdido por um, perdido por mil". English / Portuguese Dictionary, by Joseph D. Lesser, 2019.
L2: EN-US
Register: idiomatic
Proposed translations
Brazil
Trilingual translator and proofreader
Native in: Portuguese (Variant: Brazilian) 
Works in: English to Portuguese, Portuguese to English, Japanese to Portuguese, and 3 more.
nothing to lose, everything to gain/have nothing to lose
https://www.google.com/search?client=firefox-b-d&q=nothing+to+lose%2C+everything+to+gain
https://www.amazon.com/Nothing-Lose-Everything-Gain-Multimillionaire/dp/1591845998
https://dictionary.cambridge.org/dictionary/english/you-ve-got-nothing-to-lose
https://www.macmillandictionary.com/us/dictionary/american/have-nothing-to-lose
Portuguese to English, English to Portug
Native in: English
Works in: Portuguese to English, English to Portuguese
a miss is as good as a mile
Translations by lawyers for lawyers
Native in: English
Works in: Portuguese to English, English
might as well be hung for a sheep as a a lamb
The use of the word perdido connotes risk of loss.
My answer is an equivalent that works in contexts in which the risk element is paramount.
United Kingdom
www.lingocraft.co.uk
Native in: English (Variants: British, Scottish, Irish, Singaporean, UK, South African)
Works in: French to English, Italian to English, Romanian to English, and 2 more.
In for a penny, in for a pound
"used to say that a person should finish what he or she has started to do even though it may be difficult or expensive"
"If you want to quit, I'll understand." "No, I'm sure we can do this. In for a penny, in for a pound."
https://www.merriam-webster.com/dictionary/in for a penny, i...
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Note added at 10 hrs (2023-01-23 12:03:55 GMT)
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This phrase is exactly the phrase used in the heading/title of this newspaper article about a footballer, who has reportedly "thrown everything" in to win this game. if you browse through the article, you will see how the final phrase basically sums up a similar situation to your quoted one:
"IN FOR A PENNY IN FOR A POUND
BARRY Ferguson was born and raised in Hamilton ..... .....
Sasa Papac afterwards claimed Rangers were now showing the "winning mentality" that could take them to the title, but no-one who witnessed the late flare-up - Neil's hack on Naismith leading to a pointless fracas - could accuse Hamilton of not having a go. In fact, it could be said that Hamilton threw everything at their visitors."
https://www.heraldscotland.com/default_content/12759582.penn...
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Muriel Vasconcellos
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Clauwolf
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PaulaEsp
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Discussion
Even though it's not quite idiomatic, it's very much in line with the definition of "perdido por um, perdido por mil".
>> If you have nothing to lose: it is worth taking a risk because you would be no worse off if you fail, but you might gain some benefit if you succeed. Sometimes written as “nothing to lose, everything to gain.” (Charlene Dargay, Quora)
perdido por um, perdico por mil: "... essa expressão é usada quando não se tem mais nada a perder, quando uma pessoa está em uma situação difícil e só tem uma saída, que é arriscada." (WordReference)
Thank you all.
O técnico francês Henri Michel, em vez de recompor a defesa de Camarões com a expulsão de seu zagueiro Rigobert Song, hoje treinador da equipe, preferiu partir para o ‘perdido por um, perdido por mil’, e colocou o veterano Roger Milla no lugar de Embe, ganhando os aplausos da parte não-brasileira dos 43 mil torcedores presentes ao Stanford Stadium, em Palo Alto, naquele 25 de junho de 1994. (Portal A Tarde) ... preferred to go "all or nothing"... (?) (Penso que aqui o sentido seja "partir para o tudo ou nada".)
"Perdido por um, perdido por mil, o técnico Cuca sacou Mariano e entrou com Pedrinho. Posteriormente, Nacho Fernández deixou o time e Ademir foi promovido ao jogo. Mais veloz, imprimiu maior pressão, mas sem converter as chances em gols." (98Live) With nothing to lose and everything to gain... (?)
in for a penny, in for a pound: custe o que custar; custasse o que custasse; sem medir esforços https://masterportuguesetranslator.com/glossaries/dicionario...
A miss is as good as a mile: Quase ganhar é perder. It's related to "Almost doesn't count". https://masterportuguesetranslator.com/glossaries/dicionario...
I'll go over the other two before making a decision. Thanks again!