It is a pure coincidence.

Food stamps cause poverty, i.e. receiving food stamps decreases your motivation to provide for yourself and thus make you poor.

Observing correlation between poverty and food stamps does not tell us if there is any causality (and if so, in which direction). The correct answer can be any of the above or below.

Poverty causes food stamps, i.e. being poor has a causal impact on receiving food stamps.

The causality goes both ways. Being poor has a causal impact on receiving food stamps, but food stamps also decrease your motivation and thus make you poor.