Usually, students who go through a research program, aim for a research project or a project the output of which may be a research report or a scientific publication. As far as this program is only offered in a few number of universities or research centers; I just want to add some comment to the questions you asked.
In some universities, non-degree programs are offered as some students want to attend to the university not going through the official class-attending programs. I mean, in a non-degree program, the student may not have to attend all the courses offered in a degree leading program. The student has the opportunity to choose the courses he likes and the ones mostly near the field of research he likes to do. It may be noted that in a degree program, the student may have to pass a few number of courses which may be chosen by the group or department; but in a non-degree program, he has the opportunity to choose from a wide range of different courses which he likes more. I insist that that because these programs may not lead to a degree, each university may have its own regulations and the student may or may not have the opportunity to choose as many different courses as he wants. It is better to check the universities' websites.
The answer the your question about why students apply for such programs varies. Some students prefer to enjoy the freedom of the program, choosing a number of courses and pass them,while they do some research activity in the research institute. Some researchers prefer to apply for this programs as they have passed some courses before and they are coming with a good research background; so they apply for a non-degree program just to expand their researches and do some publications at the end of the research period. Some other students are the ones who work in industry and do not have enough time to attend a complete degree leading program and have a research topic in mind; so they apply for such program and do research in the field of their desire.
When we are talking about research, It means that we are looking for something new. When something is done before and the researchers looks for it; it is called research but the output may be a Review Paper not a Research Paper.
A non-degree program may differ as a matter of time. The research period may be three months, six month, one year or more. But as the research non-degree program student does research under supervision of a professor at the university; the output should be something like a publish paper, conference paper or a research report or book. If the person applies for a non-degree program and does not have any publication at the end of the research period, why does he attend the university?
The research student may take most of the research period, by talking to the other researchers and students at the university. Go to some courses and read as much as papers and reports as he can. Develop new ideas for his future projects and gain ideas to make his work better.