From a functionalist perspective in sociology, poverty must serve some sort of important role in our society. In that sense, we rely on poverty to keep our society stable. Here are two possible ways in which this happens.
First, the existence of poverty may help to reassure those of us who are not poor and make us feel better about ourselves. We in the middle class know we are not rich, but we can console ourselves with the knowledge that there are millions of poor people who are nowhere near as well-off as we are.
Second, poverty exists as a warning to the rest of us. The existence of poor people shows us that if we do not work hard and play by the rules, we too could become poor. If this did not exist, we would have much less incentive to work hard.
In these ways, our society relies on poverty because it keeps us from being angry at the rich and it makes sure we have an incentive to work hard.