When someone leaves without a goodbye, you carry on, waiting for it, watching the front door, expecting every minute to finish the argument. When someone leaves without a goodbye, you expect them, dammit, to come back.
Joan has a lot of regrets. She regrets that her last words to him were on the steps of the brownstone, yelling in his face to get out of her life. She regrets the harsh words she used, calling him selfish, a liar, detached from reality - even though every word is true. She regrets not sprinting after him and grabbing him in the street and saying for God's sake Holmes where are you going?
And she had not even known about the plane crash until the lawyer's letter arrived to give her the powers of executrix. Weeks had passed and her fury has changed to annoyance, then incredulity at his complete disregard for her, then a slow, heavy worry.
The letter was dry as chalk in her hand. It gave references and cross checks so that she might satisfy herself as to all the facts before proceeding. And then it invited her to become the manager of the Holmes estate, charging her with finding an heir since both brothers were now missing, presumed dead.
That final word made her sit down hard on the third step, jarring her spine.
Dead.
Her, shrieking hurt and fury in his face.
Dead.
Him, biting his lip and refusing to answer, his eyes flickering in the gales of her rage like the candles of an ancient lighthouse, wavering in a great sea storm.
Dead.
It was not like this with Mycroft, who was not really dead. Who now Joan had to find, and tell.
Dead.
She placed her hands one either side of her, flat on the stair, and faced the blank front door. Gone, truly gone, and he never said goodbye. She took a breath and said, because from this moment on she would have to get used to saying it in spite of the pain, "Sherlock."
She thinks often of this moment, the letter, and so far it has not grown any easier.