"What will happen to the (poor/elderly/disabled/etc. etc. etc...) in an Objectivist society?"
"If you wish to help them, you will not be stopped."
(Paraphrased from The Virtue of Selfishness)
If that doesn't make the point clearly enough... those who fear that the disadvantaged members of human society will be left to shrivel and die in an Objectivist world, thus proving how heartless Objectivism must be, should think about this question and answer. There are apparently many people in the world who think it's worthwhile to help others, and through private charities they could still be helped, as they are now.
If government money was not shelled out for any welfare, charity, grants, or other such uses, would someone asking this question still be willing to give of their own money to help others, at least an amount equal to what they would have been paying in taxes instead?
Or, no longer forced to cough up a regular donation with the government looking over their shoulder and taking care of it all for them, would they keep their money and simply bemoan the state of the world, wondering why someone else doesn't do something?
The point is not that the poor shouldn't even be allowed to be helped- the point is people should help them because they want to. Not through force. People should put their own money into where they think it can do good, not into a government pool that might put that money into places they'd rather not have it go.