Shelden claims to be the mayor because he showed up first. Even though nobody ever attempts to take over, no one really sees him as the mayor, either.
He is one of the first people the Hero meets in Passwall; he is seen heading up to the Gatekeeper with Felas Sarandas to watch a group of adventurers attempt to fight him. Besides some small tidbits of advice, he has very little to provide the Hero.
During Retaking the Fringe he will be seen again inside Xeddefen hiding from the Forces of Order. If he is allowed to follow the Hero, he will be of some use until they get split up. If he is told he needs to leave on his own, he will probably be killed by one of the Knights of Order or die during the collapse of the ruins.
The Hero, when first entering the portal on the island in the Niben Bay after being briefed by Haskill at the end of A Strange Door, will come to the town of Passwall. In town, the Hero will find two characters talking, the mayor of Passwall and a dark elf.
Thadon or Lady Syl will also tell Sheogorath that the Fringe has been taken. Sheogorath is delighted, as this is a new turn of events, and sends the Hero to investigate. They will eventually go to the ruin Xeddefen.
Xeddefen is a fairly large ruin. Look for buttons in walls, traps, and watch the map for the beginnings of hallways behind secret doors. Proceed to the Great Chamber where they will discover Shelden, the self-appointed mayor of Passwall, sneaking through the halls.
"Hello, I'm Shelden. I've been here the longest. That's why I'm mayor of Passwall. That, and because I'm the best at being in charge. Welcome to my town!"
- Gatekeeper "He guards the Gates of Madness. Don't get too close to him. He'll kill you, and it will leave a mess in my town. Jayred Ice-Veins wants to kill the Gatekeeper. Sounds like suicide to me."
- Gates of Madness "They say the keys are sewn up in the Gatekeeper's body. Basically, that means you're not getting in."
- Passwall "The place was pretty deserted when I got here. Of course, once I was here, others followed. Can't say I blame them."
- There is amber and madness ore in Shelden's House.
- If the amber and madness ore are taken it must be before doing the quest "Retaking the Fringe."
- There are also alchemical ingredients in his house.
- Shelden is wearing Purple Finery.