The Gemara notes (toward the top of amud beis) that the owners of the sacrifice achieve their forgiveness via the priests eating from the korban. The Ramah (Toras HaOlah II:25) discusses a number of features of the Asham and Chattas sacrifices that show a beautiful regard for human dignity.
Since these were sin offerings and the consumption of the sacrificial meats achieved the forgiveness, the Torah made certain restrictions to spare embarrassment of the sinner and to not create additional barriers toward repentance:
- The meat was eaten only inside the Beis HaMikdash unlike lighter sacrifices, so as to keep the sinner’s identity more hidden.
- The meat was eaten only for that day and evening, also to minimize the sinner’s embarrassment
This is an important lesson for us to keep in mind. If the Torah is concerned about embarrassing a person who sinned and repented, surely we should be even more careful about embarrassing anybody.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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Rabbi Simcha Feuerman, Rabbi Simcha Feuerman, LCSW-R, DHL is a psychotherapist who works with high conflict couples and families. He can be reached via email at simchafeuerman@gmail.com