Methuselah and Lamech, who were born before Adam died, obviously trained up their grandson/son Noah well, and in fact were still alive when Shem was born.
Shem's Cave according to tradition is twenty kilometres north of Tiberias in Safed in Northern Israel.
The *Midrash (Jewish Rabbinic literature) refers to the influence of Shem (and Eber) on numerous occasions. Each time, Shem and Eber appear as the spiritual guides of the forefathers and mothers. Genesis 25:22 describes Rebecca’s pregnancy, explaining that “the children struggled in her womb.” To understand this abnormal occurrence, she “went to inquire of the Lord and the Lord answered her” (Gen. 25:23). The Midrash here explains that she went to the beit (house) midrash of Shem and Eber. The Midrash similarly claims that conversations that Sarah and Hagar had with God took place through the mediation of Shem (Gen. Rabbah 45:10, 48:20). However, Shem and Eber are not merely intermediaries between man and God; the Midrash explains that they were figures of justice as well (including the next life). In the Midrashic read of the story, Esau feared killing Jacob because he knew Shem and Eber would judge him for this sin (Gen. Rabbah 67:8).
Finally, Shem and Eber are presented as teachers. Abraham sent Isaac to learn Torah from Shem (Gen. Rabbah 56:11). Rashi, quoting the Talmud, says that Jacob also studied at the **Yeshivah (school) of Shem and Eber. The Midrash teaches that Jacob taught everything he had learned to his son, Joseph (Gen. Rabbah 84:8). In addition to the sources in Genesis Rabbah, Shir ha-Shirim Rabbah states that one who studies Torah in this world will be brought to the beit midrash of Shem, Eber, Abraham, Isaac, Moses, and Aaron in the world to come (Shir ha-Shirm Rabbah 6:2).
Shem died 25 years before Abraham, in Isaac's 51st year. Eber died 29 years later.
It was Isaac's 80th year, and Jacob and Esau's 20th. Awkwardly, from a historical perspective, we have minimal records, other than Genesis, to Shem and Eber's lives, for that we'll have to wait for eternity.
* a midrash is "a type of literature, oral or written, which stands in direct relationship to a fixed, canonical text, considered to be the authoritative and revealed word of God by the midrashist and his audience, and in which this canonical text is explicitly cited or clearly alluded to".
**A yeshiva (Hebrew: ישיבה, lit. 'sitting'; pl. ישיבות, yeshivot or yeshivos) is a Jewish educational institution that focuses on the study of traditional religious texts, primarily the Talmud and the Torah, and halacha (Jewish law).
**End of Page