The cost is repaid.
From a US News and World Report:
Would Syrian Refugees be an economic boon or burden.
"In Cleveland, for example, local refugee services agencies spent about $4.8 million in 2012 as they helped refugees get established in the area, according to a study conducted by
Chmura Economics & Analytics. But the economic impact those refugees had on the community weighed in at about $48 million, roughly 10 times the initial resettlement costs.
The World, Visualized as 100 People
"Refugees are more likely to be entrepreneurial and enjoy higher rates of successful business ventures compared to natives," the report said. "At the local level, refugees provide increased demand for goods and services through their new purchasing power and can be particularly revitalizing in communities that otherwise have a declining population."
Granted the cost doesn't cover the screening process, but it isn't that difficult to see how it gets rewarded.
Have a look at a cost analysis from the
Brookings Institute regarding the impact on Leanese/European economies. Many of these refugees don't have UNHCR designations, but are refugees nonetheless.
EDIT: I should add, refugees are expected to pay back the cost of travel. They are given travel loan (interest free) to a U.S. Refugee Resettlement Program. After resettled, they must repay the loan.