Yes, sadly they do and it is something that should be corrected. If you leave school the money should go back to the agency that provided it not into the pocket of the drop out.
I have a friend who left teaching and decided to go back to school to get a culinary degree. She said the first couple weeks of her first two semesters were awful. When the date rolled around that allowed students to drop out but keep the money all the lazy troublemakers who were just there to get the money dropped out. After they left the class could get organized and move forward. She said the ones there for the money treated it all as a joke, arriving late, could barely read and mouthed off to each other and the instructor constantly. She said the first couple weeks of the semester were worthless. When she got to the third semester it was better because the trouble makers did not have the necessary requirements to be in those classes.
It’s not accurate to say that the student can get their money if they don’t show up or if they leave after 2 days. Not if the school is doing their job. (This is what I do for a living.)
If the student never attends, the school is required to send the money back and the student can’t have it. If the student drops out (formally or just quits coming) before the 60% point of the term, the school is required to send a pro-rated amount back.
If the school isn’t doing this, they can be cited for it, and will ultimately lose their ability to give federal aid.