Whoa, what? You did your job perfectly from the sound of things, and it’s not your fault you’re related to a bunch of grade-a free-range shitheads, nor did you invite them.

Wow, I can't imagine what your relationship must be like with your parents. Any of my close friends or family would cover a random expense if asked without a moment of hesitation.

Why would you get fired?? Being related to them doesn’t make you responsible for their actions

Based on the lack of information about why you got fired, I'd say YDI.

You should NOT have gotten fired for that. Whether they were your parents or strangers, it's not your fault or responsibility if someone forgets their wallet. And it's quite obvious that you didn't invite them to your place of employment, so it's not like you were involved other than having the unfortunate task of waiting their table. I'd fight the termination.