Albert Barnes Commentary 1 Samuel 19:24

"And he also stripped off his clothes, and he also prophesied before Samuel, and lay down naked all that day and all that night. Wherefore they say, Is Saul also among the prophets?" — 1 Samuel 19:24 (ASV)

Naked - That is, without his robe and other outer garments, but only his tunic. Compare the related verses.

This entire account provides another example of the protection God grants to His servants, which is a frequent topic in the Psalms of David.