The phrase "faces one's punishment" has several synonyms that can be used interchangeably. One alternative is "accepts their fate" which conveys that the individual acknowledges the consequences of their actions and is ready to face them. "Owns up to their wrongdoing" is another synonym that implies the admission of guilt that precedes the acceptance of punishment. Similarly, the phrase "takes responsibility" conveys a similar idea, linking consequences to one's actions. Additionally, "bears the brunt" accurately communicates the idea of enduring the full impact of the punishment. Finally, "endures the consequences" is a straightforward synonym that succinctly conveys the intended idea.