"Sacrificial offering" refers to the act of giving up or surrendering something valuable or meaningful as a way to show devotion or commitment, typically to a higher power or cause. Full definition
The Mayans made sacrificial offerings on its chest, including human blood and hearts. (lacarmina.com)
But they who by sacrificial offering, charity, and austerity conquer the worlds, pass into the smoke (of the cremation - fire); from the smoke, into the night; from the night, into the half month of the waning moon; from the half month of the waning moon, into the six months during which the sun moves southwaid; from those months, into the world of the fathers; from the world of the fathers, into the moon. (religion-online.org)
The personal sacrificial offering conducive to grace is replaced by the use of someone else's property. (firstthings.com)