One key element could be a sense of duty. The family may have felt it was their duty to serve the king and protect their country. This might have manifested in different ways, such as joining the military or providing essential services. Another element could be heritage. Their family story might be intertwined with the history and traditions of the country under the king's rule. For example, they may have held a particular title or position that was passed down through generations, and with it came certain responsibilities towards the king and the nation.
Perhaps loyalty would be a key element. The family was likely loyal to the king and their country, which could have led them to make various sacrifices.