It's a sad thing when a child grows up knowing that one of the parents abandoned him or her. Often, the child believes there is something wrong with them or that they did something wrong to cause the parent to leave. There are worse things and knowing these things can help the child cope.
The important thing is to let the child know that the parent who left is a loser. Excluding those rare cases where the parent left for some important purpose, it is almost always the case that the parent left because he or she is pathetic. It is not the child's fault. It is the fault of something in the loser's environment (poor upbringing, bad friends, etc) that caused the loser to be a loser.
Explain that the cause of the loser parent being a loser is something in the loser's environment. This way, it is not something inherent to the loser him or her self. This helps the child's self worth. After all, if the loser parent started out a loser, then there is a good chance that the child will also be a loser. If it is caused by external factors (your favorite bogey man) then the child can proudly blame those factors.
These children often want the loser to come back. Most children want a couple of parents, along with all the positive attention that entails. Address this with the message that it would be nice if the loser parent stopped being a loser and then returned, but if the parent is still a loser then everyone is better off without them. The worst situation is that the loser comes back and brings all the loser-ness with him or her. Just keep telling the child, "It could be worse; the loser could come back."
Of course, LibertyBob is not a psychologist, only a person with brilliant insight and genius. I have seen many youths go through the problem of the missing parent. It is always so sad, they say, that the loser parent doesn't come back. Well, I've also seen the results of the loser coming back. Trust me; you are usually better off without him or her. Unless that the pathetic loser parent has gotten better (really and truly better, not just claiming to be better and making promises) then the child is better off with just the one parent. Just keep telling the child, "It could be worse; the loser could come back."
The next time you face a child being raised by a single parent and the child is glum about the missing loser parent, take the time to reassure the child that he or she is better off. Let them know that the loser is that way due to the effects of your favorite social ill. Make them understand that the problem is not the child's fault. Tell them that the best thing they can do is work hard to be successful. Then tell them to sit down and shut up so you can continue what you were doing, or tell them to go get you a beer.