I can see several possibilities.
In Orihime's case, it could be that her brother had some kind of life insurance, just in case.
Considering that he worked, he also might have left some savings.
I have no idea of how these things are supposed to work in Japan, but considering her rather complicated personal/familiar situation she might get some kind of economic help from the government.
In Chad's case, he might have just inherited some money from Abuelo. Orphan =/= destitute, sometimes.