I’m particularly curious about the moral/legal aspects of serving websites run by others on one’s own machine. Who takes responsibility when illegal content is

I’m particularly curious about the moral/legal aspects of serving websites run by others on one’s own machine. Who takes responsibility when illegal content is discovered? And how does one make sure that the illegal content is not redistributed? (“Illegal” here is a euphemism for anything considered morally wrong to consume or distribute by most of society)