The fewer NEWT classes you take, the more free periods you have. Ron and Harry have quite a few free periods in their sixth year:
“Look,” said Ron delightedly, gazing at his schedule, “we’ve got a free period now... and a free period after break... and after lunch... excellent!”.
In theory, if a student was poor enough, it could be possible to pass zero OWLS. The student would apparently then have free periods all day, in which case there might be no point of the student continuing school. However, it seems unlikely that it would come to this. If a student was so poor, there likely would have been interventions earlier. The school apparently offers some form of remedial classes, as Harry is supposed to claim that he does Remedial Potions with Snape:
“I will expect you at six o’clock on Monday evening, Potter. My office. If anybody asks, you are taking Remedial Potions. Nobody who has seen you in my classes could deny you need them.”