Was David saved by spider web from saul?

yes he was saved by a spider.

In 1 Samuel 23-24, David is hiding in caves because King Saul was trying to kill him. There is a Rabbinical story (midrash) in the Talmud (learing) about about this which says that God used a spider to spin its web over the opening of the cave David was in so that when Saul saw the web he passed by cave because he knew that David could not be in there otherwise he would have broken the web. The spider was like Queen Esther, used for such a time as this. Look for the divine appointments God will use you. :)