Consider a case of a metzorah (spiritual leper) who likewise needs atonement. He gets it by bringing a guilt offering. What happens when a priest brings the offering for the wrong reason? - The offering is valid but does not count for its owner. Now we have a problem: we cannot ignore what was done and bring another sacrifice because it would then be two offerings for the same purpose, and that is not allowed. This metzorah never gets his purification. He has "no remedy."
That is not the only case of no remedy. Consider a Nazirite who is completely bald. The school of Beit Shammai says that he still needs to shave his head. However, since he has no hair, this need cannot be fulfilled, resulting in no remedy.
(Luckily for the people in question, the law does not follow these opinions.)
Art: Portrait of a Bald Old Man by Rembrandt