As for unalienable rights, the republican government of the US passed the Patriot Act and its amendments. This republican government does not view your rights as inalienable either. This is reality. This republican government thinks you have to give up your inalienable rights in order for them to protect you from suspected terrorists.
So what really would hold a pure republican government responsible to the people is a mixed democracy where the people can at least call for a referendum if something like the Patriot Act passes. Just this possibility will go a long way toward having real individual justice as well as social justice. Why, because if politicians know something will lose in a referendum then they will try to get it right before a referendum occurs.