The phrase "gives his walking papers" typically refers to ending someone's employment or firing them from their job. There are a variety of synonyms that can be used instead of this phrase, such as terminating employment, dismissing, laying off, letting go, releasing, or sacking. These terms all convey a similar meaning of ending someone's work agreement or relationship with an employer. However, it's important to consider the context and tone in which these words are used, as they can have differing implications and levels of formality. Ultimately, choosing the right synonym will depend on the specific situation and the desired impact of the message being conveyed.