There are several different Island Events that can bring new villagers to your game (babies or adults), so it's never hopeless until all of your villagers have died. One way to give yourself the best chance of getting one or more new villagers is to set your game speed to Slow. You'll get more Island Events during your remaining villager's life when the game is running at the slowest speed. If your last villager does die before any new villagers arrive in an Island Event, you will need to start the game over.
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