It's difficult to assess much in way of blaming Eliezer's family for opportunities not taken prior to their deportation. Yet, there were some distinct moments that could have been seized. Moshe the Beadle's warnings could have been taken more seriously than they were. Moshe gives "actionable intelligence" in which more people of Sighet could have acted quicker in escaping what was awaiting them. Additionally, the maid, Maria, offers sanctuary to Eliezer and his family, only to be rebuffed in her attempts. This could have been an avenue that was pursued. In much the same way, the Hungarian police officer who tapped on their window before the move to the Ghetto was an opportunity to escape that was not taken. A more structural answer to this question would be present in Eliezer's family, who was so much more concerned with the welfare of the community and the other Jewish people in Sighet that he failed to account to the dangers to his own family. This precluded him from taking action to save his family. As stated before, I think it is really difficult to assign any sort of "blame" to Eliezer's family, as the real blame must be shouldered by the Nazis. Yet, Wiesel does depict moments where paths presented themselves and given the horrific account of what is in the narrative, it is almost human nature to wonder about what could have been as opposed to what was.