If loneliness refers to the state after breaking up, lingering fragrance should be the memory of falling in love or something. The lingering fragrance is also fragrant, indicating that this memory is beautiful, indicating that she misses it when she is lonely now. I think there are two possibilities. More likely, she wants to show that she can face up to your breakup and get over it slowly. The smaller possibility is that she wrote it to you. I hope you can contact her. The key is to see what kind of person she is at ordinary times, and whether she likes to transmit information rather than communicate in this way. If she is a cheerful and lively girl, this signature is the first possibility I said.