To what extent should we take responsibility for things that happen after we die? Epicurus himself made arrangements for the school and his parents memory in the event of his death so the answer is not "not at all". I think the Epicurean perspective suggest that we should only do so as far as is required to live up to commitments made during our life. We can also take actions that will benefit people we like, such as our friends and children. But do we owe unborn great-grandchildren anything?
The clearest example is perhaps climate change, which I understand will keep having worse effects as time goes on. I have children and will likely get grandchildren during my lifetime. This makes me want to support at least some green initiatives. But where does the responsibility end?