Aruch HaShulchan, The Laws of Tzedakah, 250:5

If our situation is good and there are many wealthy people in the city, and the poor are few, then of course the obligation is on the public as a whole and not on individuals, but also the individual can, alone, fulfill their needs. In any case, it is incumbent on everyone, and this is the intention of our teacher Rabbi Moses Isserles. All this refers to the tzedakah collector, because he alone acts on behalf of the city or the public. However, no individual alone is obligated to give ‘according to their needs’ even if that person has the means, when there are other rich people in the city, and even if the poor come to the wealthy person. That person should inform everyone else, and everyone should give. Truly, if the public does not come to their aid, for example if they (the other wealthy community members) are out of town or if the wealthy person lives alone, then they alone must provide if they have the means. And so, if the others do not want to give and the wealthy person has no way to force them, then the obligation falls on that person alone. [Translation by Rabbi Bruce elder. Edited for gender neutrality]