GERMERING, Germany—Valmir Sahiti, 25 years old, has spent the last two weeks living in a nursing home in the long-shot hope of a new life.

Mr. Sahiti, an asylum-seeker from Kosovo, is staying with five relatives in a makeshift refugee center set up on several turquoise-carpeted empty floors of the home. He says he is aware the German authorities may soon send him back, but he insists the chance to live in Germany is worth the attempt.

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