you are right - there is such a word that absolutely corresponds to the meaning you intend to express. This word is famish and, according to Collins English Dictionary (8th ed.) it means 'to die or cause to die from starvation'. However, please mind that in this meaning it is somewhat archaic, so use it where appropriate. There is also a word perish,
A few comments on "famish," "perish" and "starve":
I had never heard of "famish" as a verb meaning "to die of starvation." I looked it up, and it is definitely archaic. On the other hand, "famished" as an adjective meaning "very hungry" is commonly used. If I heard the sentence "he famished," (meaning he died of hunger) I would assume the word was being used incorrectly.
Thanks everyone I think I had a misconception about this word.In Jainism there is a trend of dying by starving until death after a certain age or when a person has made himself free form all bondage of life and wishes to die.In my language there is a single word for this so I thought that there might be such a word in English also