That definition might stop working. The important thing is whether you can afford food, clothing, shelter, required transport, and still have some money left over to take care of everything else.
But that definition might not stop working. If you calculate the poverty line as, for example, median income multiplied by 0.6, it is possible to have every single person above that line.
Poverty is usually defined in relation to others in your community. A poor American is richer than a poor Nigerian. So it won't eliminate poverty =)