Can an employee be dismissed due to a relative working in the same company?

I recently read a story about a woman who was fired from her job simply because her mother also works at the same company, and the court later deemed such dismissal illegal. What if I'm in a similar situation: my relative and I work at the same company, and management is offering me a demotion to a worse position due to changes in internal rules, and if I don't agree, they threaten dismissal. Do they have the right to demand this from me (to step down from my position or dismiss me simply because I am a relative of one of the employees)?