Firstly, "leftover" doesn't unambiguously refer to food as in "last night's leftovers in the fridge".
A leftover anything is something that remains. For instance, "Bob went into the building one more time to grab a few leftover boxes and items, and then shut the door for good."
If the "leftover" is turned into a noun, and particularly if subsequently pluralized to "leftovers", then it has a stronger association with food: that word refers to uneaten food more often than not.
Outside of any context, "leftover woman" will not be unambiguously interpreted as an unmarried older woman. It could be a woman left behind in any conceivable situation: "Everyone was rescued from the island, except for one leftover woman."
But in a discussion about unmarried women, if the term is introduced, it will be clear what it refers to; and it will have a negative connotation, laced with sexism, possibly deeply offensive to some people. It has the interpretation of insinuating that a woman is just an item, and one without a husband is just an uncollected or unconsumed item.
"I want to use the word "spinster", but it is a negative word."
But you started this discussion with a negative Chinese word. If that Chinese word has connotations that a woman is just an item, and an unmarried one is just a wasted, unconsumed item, then "leftover woman" actually works. If it doesn't have connotations which are that bad, then "old maid" and such may be more appropriate.
In any case, the job of a translator isn't to produce a sugar-coated version of a text in another language.