Or do people have moral responsibilities, and the government only has legal responsibilities?
I think that approach makes some sense. I can't fault someone for trying to do the right thing and being saddled with the mistakes of the past. There's no way you can have a moral responsibility to perpetuate an injustice merely because your predecessor agreed to it, particularly if you got the job by telling people how much you don't like the way it used to be done.
Democracies can't bind the future an infinite amount. That requires a level of wisdom in the public that will simply never be on offer. We don't even ask that people always keep their own promises, even though we know they generally ought to. I'm not sure we should ask people keep promises they didn't even make – which is what continuity of government policy might ask of us.
But let's consider some recent examples, see if our intuition matches our model.
What about Brexit? There were years of delay because the republic, as an institution, didn't want a policy, but decided to hold a referendum. My guess is that many, or most, didn't care very much one way or the other. But if they did, would they be bound by the previous promise to abide by the results of the referendum, even if they, specifically, didn't make that promise? I don't think so. I think, if you don't like a politicians policy, they vote them out. If you haven't done that, they should use their best wisdom to figure out what to do, when it is truly within their power. If you said you'd follow the referendum, then do so, but if you didn't, know that you're trusted to make choices on your own.
What about Britain's responsibility towards Hong Kong after the transfer to China? The Chinese made an agreement, and have not truly lived up to it. Hong Kong should be independent of Chinese control for several decades to come, but they are not. What's Britain to do?
I strongly support Britain using their new found independence of the EU to give Hong Kongers citizenship, no questions asked. But in terms of their moral responsibility, I'm not sure they have one. If they do, I'm a bit at a loss as to what's required of them. Do they have to try and retake Hong Kong? Seems absurd. And if you don't know what your moral duty entails, it's possible you just feel guilty – as well Britain should. But moral duties are typically less opaque.
What about jurisdictional issues over e.g. helping Iraqi translators who helped American soldiers? If there is no moral obligation, does the US government have legal responsibilities outside of the US, and if so, how would those legal responsibilities even get enforced?
On this point I can only say, my conception of legal duties is not so specifically bound to the specific vision of American law seen in use today. I think the American government ought to be bound by promises it makes to foreigners, and not being able to cut deals efficiently in the international context hurts American interest.
This model isn't perfect, I suppose, but it gets us decently coherent ideas about what we owe to each other.