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UTICA, N.Y. — Over the past few decades, as a manufacturing decline left homes vacant and storefronts dark, New York’s upstate cities opened their doors to refugees. The influx, while modest, gave new life to neighborhoods, helped alleviate labor shortages and shored up city budgets.

But that rejuvenating bounce for cities such as Utica, Buffalo and Syracuse ended after the Trump administration drastically cut the number of refugees allowed into the country. New York received 1,281 refugees in the last fiscal year, compared with 5,026 just two years before, according to the State Department. Officials in those cities worried they had lost a small but important bulwark against population decline.

Now, some are testing out a new strategy: luring refugees who have settled in other parts of the United States to move to New York. They are advertising job placement, English language and housing services, hoping to draw enough people to offset the shortfall.

New York is not alone in trying novel ways to reverse its dwindling population. Maine, for example, has offered an outstretched hand to refugees in hope of expanding its work force. Vermont has dangled $10,000 grants to entice people to move to the state and to work from home, in a bid to attract young tech workers. And Wyoming is trying to woo people born there back home by deploying recruiters to help them find jobs.