A wife does not greet her husband at the door. In Targum Pseudo-Jonathan on Genesis 23:2, the Aramaic names what Abraham finds when he comes down from the mountain: Abraham came from the mountain of worship, and found that she was dead.
The Hebrew text is more opaque — it simply says Abraham came to eulogize Sarah and to weep for her. The Targum of Pseudo-Jonathan fills in the journey. He came from tur pulchana, the mountain of worship, which is Moriah. He has been walking for three days since the Akeidah. He does not know yet that his wife has died. He arrives. She is already gone.
The rabbinic tradition reads this sequence as the full cost of the binding. Sarah died hearing news of her son's near-sacrifice. Abraham returns triumphant to find his partner in the covenant silent forever. The aliyah to the mountain has taken a price that did not appear on the ram's back.
And then the Torah shows what the righteous do. He sat to mourn for Sarah, and to weep for her. Not one verb but two. First the public eulogy — sifda — then the private tears. The Targum preserves the order: the community first, the grief after.
The Maggidim took this as the origin of Jewish mourning custom. The takeaway: when you lose someone, do both. Speak their eulogy so others can remember them, and weep privately so your own soul can release them.