I kind of want a Lost in Blue-esque game, but more... RPG-y.
Let's use the whole shipwreck thing, that's how you wind up on a deserted island. You'll get six characters, each with three "abilities" at start. These aren't any supernatural or otherwise strange abilities, but could be something such as knowing various toxic mushrooms or knowing how to fish well. You can choose one for each, but the other two are random.
Next, each character is assigned different stats- strength, intelligence, etc. that affect certain skills. Climbing, for instance, requires good Strength, someone with high Intelligence will be able to build better things from available material, etc.
The game can be played one of two ways. There are many jobs to do, as well as explore the island. You are able to play as one character through the game, the others doing things they're good at as they need to be done under your lead. The other way is ad-hoc multiplayer that can be played on and off, over live. THe game saves if someone disconnects or players decide to end the game, and may only be picked back up if all players are back (or, if needed, an AI can stand in for 1-2 players.)
The island is big and has lots of secrets. Most are randomly generated based on the islands, again random, history. You may find a huge, broken cannon and various plane wrecks, indicating a WWI/WWII era war. Maybe there's a broken-down lab underneath parts of the island, where secret testing was done. It may be a completely untouched island.
The goal can be set, though starts off as "Build a radio/communication method", then survive for 40 days after using it.
Each day, every character needs water, food, and a place to sleep. They may also need medical treatment.
Characters develop relationships via chatter, doing things for one another, etc. While relationships generally give only minor boosts to interactions, they can boost morale even with uninvolved characters, which will promote survival. If everyone lets the fact they're stranded get to them, stay away from one another, and start having nightmares, it won't take long for them to go insane.
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In multiplayer, you're able to handcraft your own character.