A negative right is a right to be free of something. The opposite concept is positive rights.
In order for someone to fulfil your negative right to life they simply must not murder you. Failing to help someone is not a violation of the negative right to life.
John Locke, considered the father of libertarianism, was an adovcate of negative rights. He supported the negative rights to life liberty and property. The founding fathers of the United States drew upon Locke while writing the Declaration of Independence and the Constitution.
Ayn Rand was a staunch advocate of negative rights. According to Rand "A “right” is a moral principle defining and sanctioning a man’s freedom of action in a social context. There is only one fundamental right (all the others are its consequences or corollaries): a man’s right to his own life." 
". . .—the source of man's rights is not divine law or congressional law, but the law of identity. A is A—and Man is Man. Rights are conditions of existence required by man's nature for his proper survival"
- Negative and positive rights at Wikipedia