There are two basic types of dishonest stories about becoming homeless. There is the kind that goes on way too long, and there is the kind that doesn't go long enough. Both start out innocently enough with something like, "I think I'm about to become homeless and need some advice." Or, "I just became homeless and I don't know what to do, can you help me?"
The long story teller can be interesting to listen to, at least at first. But then you realize that, most likely, the person is not going to stop telling his story until he gets something out of you. The long story teller is usually a veteran of the streets. He may say he wants help getting off the streets, or help from becoming homeless, but what he's really doing is panhandling. He'll tell you whatever he thinks you want to hear, what will motivate you to be generous towards him. He'll tell you all sorts of meaningless details that really have nothing to do with homelessness, but is calculated to increase your sympathies. The more he talks, and the more you listen, the more he figures you for a mark, and will be able to get something out of you. If you respond by quickly giving him money, even before he's gotten very far in his story, he'll figure that he can get even more out of you if he continues talking. It is best to quickly communicate to this guy that you're not interested in hearing it, and then ignore him. Usually he'll move on to easier prey.
The short story teller usually has almost no details to share about being or becoming homeless. There is usually one of two reasons for this. He may just be experimenting with the idea of being homeless, he's testing out the sound of it for himself, and testing to see how people respond to him saying it. He may very well be having some difficulties financially or with living arrangements, but isn't really in danger of becoming homeless.
The other reason for the short story would be that he is homeless but doesn't want to confess to the real reasons for his homelessness. In this case he knows that he'll be told to confront these issues, issues that he is unwilling to deal with. Any attempt to actually help this person will be wasted because he's not ready to do what's necessary to address his problems and leave homelessness.
Regardless of the reason for the short story, the person believes there is mileage to be gained, personally or financially, for just bringing up the subject of homelessness. And, a very short story is easily retractable with "I didn't really mean it like that," in case you take his declaration more literally than he does.
So, what is a genuine request for help with homelessness, you ask?
Sincerity in the discussion is almost palpable. There is no B.S. in the story. The person gets right to the point, describes the major events that lead them to homelessness, all without extraneous detail. When telling their story they are usually shy from the humiliation of it. But they are forthright and direct in their desire to find a solution. They don't play around and waste time by talking to just anyone about their situation. They are not flippant about it. Instead they go directly to people they believe can provide help, not just to commiserate or give advice. When suggestions are given to them, they take them seriously and make every effort to apply them. People genuinely desirous of getting out of homelessness will use every resource available to them. Anything short of that and you can be certain they are dealing with more problems than homelessness.