Why do we say "While there's life there's hope"?

Meaning:

As long as you are alive, there is hope as your situation may improve

Background:

Modo liceat vivere, est spes
While there's life, there's hope
- Heauton Timorumenos (The Self-Tormentor) by Publius Terentius Afer

Comic playwright Publius Terentius Afer, (generally known as Terence to English speakers), died in 159 B.C. at about 30 years of age having written six plays that we know of. Terence was brought to Rome from Africa as a slave by the Roman senator Terentius Lucanus, who educated him and, later, impressed by his abilities, freed him. This quote comes from Heauton Timorumenos which scholars believe to have been his second or third play. There is some debate as to whether Terence originated this play or translated it in all or part from a play of the same name by Greek playwright Menander who died in 290 BC. Menander wrote over a hundred comedies but his version of Heauton Timorumenos has survived only in part.

Sometime later, Roman orator and statesman Cicero (106-43 BC) is quoted as saying: Aegroto, dum anima est, spes esse dicitur: It is said that for a sick man, there is hope as long as there is life. This was translated into English by biblical scholar Richard Taverner as part of his collection of proverbs in 1539. It is also included in English naturalist John Ray's 1670 collection.

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