Adullam in Fausset's Bible Dictionary

A city in the shephelah, or low country between the hill country of Judah and the sea; very ancient (Genesis 38:1; Genesis 38:12; Genesis 38:20); the seat of one of the 31 petty king smitten by Joshua (Joshua 12:15). Fortified by Rehoboam (2 Chronicles 11:7) Called for its beauty "the glory of Israel" (Micah 1:15). Reoccupied on the return from Bahyhm (Nehemiah 11:30). The limestone cliffs of the shephelah are pierced with caves, one of which was that of Adullam, David' s resort (1 Samuel 22:1; 2 Samuel 23:13; 1 Chronicles 11:15). Tradition fixes on Khureitun as the site, S. of the wady Urtas, between Bethlehem and the Dead Sea. This cave on the borders of the Dead Sea six miles S.E. of Bethlehem (his parents' residence) would be more likely as the place whence David took his parents to Moab close by, than the region of the city Adullam in the far West. Names of western places are sometimes repeated in the East. David's usual haunts were in this eastern region...

Link: https://bible-history.com/faussets/A/Adullam/