I never got a chance to participate in this thread while our friend moremojo was here, and I'd like to reopen the question here. The last scene of the movie echoes the work of a Japanese filmmaker named "Yasujiro Ozu, who lovingly detailed the daily domestic world of his middle-class characters, sometimes paying as close attention to the accoutrements of their environment as to the human beings wielding them. His famous 'pillow shots', wherein the camera lingers on a space after the human inhabitants have departed, are a salient example of this." (quoting moremojo)
In a way, both Ozu and Lee seem to be saying that the objects left behind by those departed not only remind us of them but carry on their spirits in some way. The simple everyday objects have a way of telling the stories of these people who went before, so that we can learn from them and apply to our own lives.