A measure of relative poverty defines "poverty" as being below some relative poverty threshold. For example, the statement that "households with an accumulated income less than 60% of the median equivalized household disposable income are living in poverty" uses a relative measure to define poverty. In this system, if everyone's real income in an economy increases, but the income distribution stays the same, then the rate of relative poverty will also stay the same.
This means, by its very nature, that there will always be a family living in (relative) poverty, even if they have a very high living standard.
Relative poverty measurements can sometimes produce odd results, especially in small populations. For example, if the median household in a wealthy neighborhood earns US$1 million each year, then a family that earns US$100,000 would be considered poor on the relative poverty scale, even though such a family could meet all of its basic needs and much more. At the other end of the scale, if the median household in a very poor neighborhood earned only 50% of what it needs to buy food, then a person who earned the median income would not be considered poor on a relative poverty scale, even though the person is clearly poor on an absolute poverty scale.