NANTUCKET — Pauline Skok was struck by the beauty of this island the first time she stepped off the ferry, on a work assignment in 2016. So after years of working as a traveling nurse, she decided to take a job at Nantucket Cottage Hospital.

Skok knew that this summer playground of the upper crust, with its historic charm and picture-perfect beaches, had a shortage of affordable housing. But she was not prepared for the struggle she would face next.The veteran nurse wanted a stable, year-long lease — but instead drifted through eight residences over two and a half years. Every time she moved, she wondered: “How much more can I do?” Skok’s experience is so common that it has a name — “the Nantucket Shuffle” — and the local hospital, a major employer on the island, is taking an unusual step to address it.