When answering a negative question with あまり, it will normally be the positive (by japanese rules). For example:
person A: 彼に来ないで欲しいですか？
person B: あまり
By literal translation, person A is asking person B, "Do you want him not to come". And person B reply when translated to english means "not really". In other words, person B (somewhat) wants him to come. Since the question is negative and the answer is also negative. This holds when following basic japanese rules. But I get the impression that person B あまり might also mean "あまり来ないで欲しい" which means "I do NOT want him to come". The question is, when one answers a negative question with あまり, does it mean the former "I WANT him to come" or does it mean the latter "I do NOT want him to come"