Theoretically it is not impossible. In most of the countries, we have three classes of people - rich, middle class and poor. But there are some countries where the poor doesn't exist. I am talking about countries such as Switzerland, Monaco and Singapore. These countries have smaller population, and as a result the governments are able to provide the basic necessities to the population. The same can't be said about overpopulated countries such as Bangladesh or Nigeria.
Poverty is being used in a relative sense. Those people who are considered as poor in Switzerland or Japan will be considered as "super-rich" if they settle down in countries such as Mali or Niger. On the other hand, many of those who are considered as upper middle class in countries such as India and Nepal would be downgraded to "poor" if they settle down in Singapore or Hong Kong. Therefore I have a feeling that rather than measuring poverty among the individuals, it will be better to talk about poverty at a country level, after studying the net wealth and average salary of the citizens.