Because, in English, for a thing, we would say "it" 99% of the time. To an English speaker "her" refers to a woman or a girl and the translation just sounds creepy.
Wow, my first thought was human trafficking also... But, of course, there is no word for "it" in Romanian. If this sentence refers to an inanimate feminine noun then the English translation would be "How much would you give for it" probably more than 99% of the time. We only really use the female gender for ships and maybe for cars (although women often tend to give their cars male names). There really is no palatable version of "How much would you give for her" in English - it just sounds so wrong.
You can also give in the sense of sacrificing something for someone. This is something that a person in love will often do to prove their love for someone. I think that is the context that this sentence would actually be used in. Althouhh then the translation should be 'how much would you be willing to give up for her'