What charitable organizations?
You just brought out solutions. If people feel there aren't enough charitable or private organizations setting out to help seniors live in dignity, then its time they are created by activists. Not only could they take in monetary donations, but also they could ask for prescription drugs people have that are not in need anymore and should not go to waste. This is just a start.
Here is an example: http://www.freemedicineprogram.com/
I would imagine that providing for the General Welfare of the United States, would include providing for the general welfare of its citizenry.
A communist might look at it and tell us that "general welfare" meant that the government must provide a job to everyone or that health care must be free. I want to see a definition of what "general" welfare meant in the constitution.
Dig up Tom Jefferson and ask him, until then, the definition for general welfare is quite clear, and it includes helping the elderly of the nation from being forced into becoming charity cases, victims of circumstances beyond their control.