Aruch HaShulchan, Laws of Tzedakah 251:4

We have already explained in another place that the ruling of the Shulchan Aruch, stating that one is not obligated to give tzedakah until he has earned enough to support himself, deals only with fixed gifts such as tithes. Everyone – even a poor person who is sustained by tzedakah – is obligated to fulfill the basic mitzvah of tzedakah by giving at least a third of a shekel each year. Now there is something fundamental about the details of the laws above that troubles me deeply. For if we explain the texts that I have cited according to their simple meaning – that certain groups are prior to others – they imply that [one may distribute the entirety of one’s tzedakah money to one group within the established hierarchy] and need not give at all to those who fall outside of that particular group. But it is well known that every wealthy person has many more relatives who are poor, and how much more is that true for people whose tzedakah funds are scant! And if this is the case, poor people without wealthy relatives will die of starvation. Now how is it possible to say this? Therefore, in my humble opinion, the explanation of [tzedakah priorities] is as follows: Certainly every person, whether of modest or significant means, is obligated to give a portion of his [or her] tzedakah money to needy people who are not relatives. But to his [or her] poor relatives, he [or she] should give a greater amount than is given to those who are not related. And so on along the ladder of priorities. Regarding that which is stated that a person’s own welfare comes first, if that is explained according to its plain meaning, then most people would be exempt from the mitzvah of tzedakah altogether, excepting the one-third shekel per year. If only it were the case that most Jews could earn enough to meet their needs! But [seeing that they do not], should all but the wealthiest be exempt from tzedakah?! And in places where there are no wealthy residents, should people be left to starve? How is it possible to say this? Nor do people act this way. [translation by Rabbi David Rosenn, AVODAH: The Jewish Service Corps]