We can imagine milly's "stranded star" to represent any number of things, like a cosmic star, an actual starfish, or even a person's fingers. The personification of "five languid fingers" helps to bridge the gap between human beings and nature, making milly's loneliness a little less lonely. The starfish looks stranded in the same way a person might feel when it seems as if they're all alone in the world. But, as we see here, we're never really alone.
Lines 5-6: The fact that milly "befriends" this stranded star tells us that she maybe recognizes something familiar about it. And since it looks lonely, we can imagine that maybe milly is feeling lonely too. After spotting the starfish, though, perhaps her loneliness doesn't feel so bad after all.