Randy is one of several playable characters from Illbleed, found in the Woodcutters section. He would later go on to appear in WWE 2K14.
Before going to Michael Reynolds' Illbleed theme park, Randy's personality appears to be that of a stoner, with a stereotypical "surfer" voice. Upon entering the park Randy is captured by Trent and the woodcutters, and is brainwashed into becoming a woodpuppet.
While it's required to save Randy, it's optional whether or not you get his brain back. Somehow or other, the protagonist is able to surgically put his brain back in, largely by the same logic of Randy being able to function without a brain in the first place.
Randy becomes a fairly standard protagonist if allowed to keep his brain, but without it he is extremely underpowered as he has absolutely no adrenaline whatsoever. There are parts of the gamewhere the protagonist speaks with voice acted dialogue - if the player is Brainless Randy, the protagonist will spout meaningless garbage. Other characters will continue conversations as normal and not acknowledge Randy's lack of a brain. This is best showcased in the Killerman section of the game, which SuperGreatFriend dedicates several videos to.
Randy returns in his brainless form in WWE 2K14 as the first opponent for Killerman in the King of the Ring tournament. Like other minor characters who show up for the tournament, Randy gets no dialogue, but this is actually quite in-character in his case. He brings a chainsaw in his entrance, probably still quite bitter about Woodcutters, but he is unfortunately not allowed to use it in the ring. He ultimately loses to Killerman, though gives him a decent fight.