The Underwear Outfit is a gag costume - consisting of a pair of boxer shorts with hearts on them - given to Toni Cipriani in Grand Theft Auto: Liberty City Stories as a bonus prize for completing the first of the game's unique stunt jumps. It has no storyline use or benefit to the player except as a novelty item.
The only other major occasion in which a player character can don underwear is Trevor Philips in Grand Theft Auto V. This outfit cannot be chosen by the player, but Trevor may be encountered in various random situations when switched to from another protagonist in which he's in his underwear for some reason. There is also a random encounter that may result in Trevor being left in his skivvies. In both cases Trevor continues to wear the "outfit" until he changes clothes at a safehouse or buys clothes in a store.