why would elisenda let out a sigh of relief for both the old man and herself at the end

Elisenda is relieved when the Old Man flies away because she no longer has to worry that he will die at their home, and because he had become quite an annoyance to her. He had long since ceased to be a curiosity in town and no longer brought them financial gain. Thus, it was a relief to be unburdened of his presence. His leaving meant  "he was no longer an annoyance in her life but an imaginary dot on the horizon of the sea."