In Tamil, there is a proverb that translates to something like this:
A tiger will not eat grass, no matter how hungry it is.
It essentially is used to describe a situation in which no matter how dire of a situation you're in, you will not use your last resort. In this case, it's used to describe that even if a tiger is starving to death, it won't eat grass (because it's a carnivore). I really couldn't find any sort of English idiom that can accurately describe this Tamil proverb. Please post all related English idioms as answers, even if they are only partially accurate.
A possible situation I might use this in: Alice was a hardworking student who believed that she could receive an A in her class without using extra credit.
I might use the idiom to describe Alice in this situation, as she refuses to use her last resort (extra credit), no matter desperate she is (because she believes she can earn an A without extra credit.)