In objectivism there is no place for charity, but there is a place for Symbiosis. There is no obligation to help, but one can (and usually would) help if it is an investment. Such is the society that Galt and his worthy contemporaries create in Atlas Shrugged. There is the supremeness of the Self, but it is supported by a firm fairness.
Charity is an opium that benifits only those suffering from the painful guilt of mooching, cheating. It does not help anyone in the medium or long runs for sure.
A practising objectivist has no guilt to wash, and thus does not need to give charity. An objectivist will live by his sweat or die in "honor".
Although it may not be the street dwellers' fault to be living on the streets, their existence does not obligate the better-to-do to give them charity. the key word is obligation.
An objectivist might try this much (if he/she sees potential): ask the begger/demander of charity if he wants work (people can usually always find something worthwile for someone to do for them) The reaction to this offer is a clear indicator of the worthiness of a person to survive as a human being on earth.
There is also recognition for biological limitations. If a being has the potential to excel in ANYTHING, an objectivist would have the keen eye to see this potential, and there is always a place for excellence.
A man without limbs can use his brains. A man without a healthy brain would fall at the fringes of Rand's philosophy. But I do not believe this example breaks her no-charity postulate. Such a "mentally special" person can (with "help" from his kin) contribute to the development of neural/cognitive sciences.
Every entity has a positive purpose from which it derives the right to exist. This purpose is determined by a combination of physical and attitudinal factors. begging ofcourse, is not a positive "purpose", as it is parasitic in nature, not symbiotic.
Would an objectivist give a morsel to save someone's life? the answer depends on the objectivist's perspective of the receiver of this gift: will the receiver, having taken my gift, exist on as a worthy contributor to me and himself? becoming self sufficient AND rewarding me for my "kindness"? if so, then my giving is not charity at all, it is investment.
If not, even if I do give charity, it is going to be useless, a waste of my resources, and the gain of no one. A purposeless being can acquire purpose by being converted to ashes/soil. then it provides the nutrients for plants, supporting the food cycle.