Answering a Knock on the Door
Answer: Generally speaking your problem is touched upon in Shulchan Aruch (Yoreh Deah 249:4) where we learn: "If a poor man asks for money and one does not have anything to give him he should not reprimand him nor raise his voice to him but should rather speak kindly to him and show his kindheartedness to indicate that he would like to give but cannot do so."
In addition to these words of the Beit Yosef the Rama writes: "It is forbidden to turn away the poor man with nothing, even if all he has to give him is a simple dried fig."
Applying these rulings to your situation we must assume that the poor man knocking on your door is equivalent to one asking for money. It is then proper to answer the door and offer the little you have, or nothing at all, along with the explanation spelled out in the Shulchan Aruch. It is also a good idea to express empathy for a person reduced to knocking on doors for help and to offer a blessing for an improvement in his situation.