The majority of homeless aren't lazy. Instead, a whole lot of them have severe mental issues, causing them to be incapable of holding a job. You also missed a

The majority of homeless aren't lazy. Instead, a whole lot of them have severe mental issues, causing them to be incapable of holding a job. You also missed a large category of jobs, which is retail. And most people working retail are not immigrants. All you need to do is be reasonably presentable for these jobs.