What is Tree in Yoli's yard?

The tree in Yoli’s yard becomes symbolic of Elf. Just as the tree is losing its limbs and withdrawing into its trunk Elf is cutting her ties to society. She is no longer doing her concert. She not only no longer speaks to fans, she doesn’t answer the phone, and while she reads Yoli’s letters, she doesn’t write back. The only way to communicate with Elf now is in person. Like the tree, she has been stripped to her trunk. It is implied that the next step is to cut down the tree now that it is dying. A person cannot live in solitude.