David leaves the Cave of Adullam and moves about in the wilderness. For example:

David continued to live in desert hideouts and the backcountry wilderness hills of Ziph. Saul was out looking for him day after day, but God never turned David over to him. David kept out of the way in the wilderness of Ziph, secluded at Horesh, since it was plain that Saul was determined to hunt him down. (1 Samuel 23.14, 15, MSG)

You should have an idea of the kind of area David was in.

Because of its lack of water and good routes, the Judean wilderness has been (mostly) uninhabited throughout history. Consequently it was an ideal place for those seeking refuge from enemies or retreat from the world. When on the run from King Saul, David hid in various places in the Judean wilderness (the Wilderness[es] of Ziph, Maon, and En Gedi are part of the Judean Wilderness). – https://www.bibleplaces.com/judeanwilderness/

David’s hiding was complicated by the fact that the folks who did live there were often eager to hand him over to Saul:

Some Ziphites went to Saul at Gibeah and said, “Did you know that David is hiding out near us in the caves and canyons of Horesh?…So whenever you’re ready to come down, we’d count it an honor to hand him over to the king.” Saul said, “GOD bless you for thinking about me! Now go back and check everything out. Learn his routines…Scout out all his hiding places. Then meet me at Nacon and I’ll go with you. If he is anywhere to be found in all the thousands of Judah, I’ll track him down!” So the Ziphites set out on their reconnaissance for Saul. Meanwhile, David and his men were in the wilderness of Maon, in the desert south of Jeshimon. (1 Samuel 23.19 – 24, MSG)

Note: God is with David; he is NOT with Saul, despite Saul’s flippant use of God-talk: “God bless you for thinking of me!”

I wrote earlier that God had to protect David and his reputation, and he used various means to do it. In this case:

Saul and his men arrived and began their search. When David heard of it, he went south to Rock Mountain, camping out in the wilderness of Maon. Saul heard where he was and set off for the wilderness of Maon in pursuit. Saul was on one side of the mountain, David and his men on the other. David was in full retreat, running, with Saul and his men closing in, about to get him. Just then a messenger came to Saul and said, “Hurry! Come back! The Philistines have just attacked the country!” So Saul called off his pursuit of David and went back to deal with the Philistines. That’s how that place got the name Narrow Escape. (1 Samuel 23.25 – 28, MSG)

God can even use the enemy for his purposes!

The king’s heart is a stream of water in the hand of the LORD; he turns it wherever he will. (Proverbs 21.1, ESV)

And there’s a psalm:

A David psalm, when the Ziphites reported to Saul, “David is hiding out with us.”

God, for your sake, help me! Use your influence to clear me. Listen, God—I’m desperate. Don’t be too busy to hear me. Outlaws are out to get me, hit men are trying to kill me. Nothing will stop them; God means nothing to them. Oh, look! God’s right here helping! GOD’s on my side,…You got me out of every scrape, and I saw my enemies get it. (Psalm 54.Intro, 1 – 4, 7, MSG)