If the job is at all comparable, particularly in terms of what it pays--then yes, she will probably lose her unemployment benefits. One of the requirements of unemployment compensation is that the recipient be willing to take more or less comparable positions if offered. So if your wife is currently in an administrative or secretarial-type position, and if the job she's being offered is within the same broad salary band or range as the jobs she's had before (it doesn't have to pay as well; it just shouldn't be shocking lower), then if she turns it down, she may make herself ineligible for unemployment insurance. People who are out of work are not allowed to hold out for the ideal placement situation. Good luck.