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The governing principle here is that unemployment benefits are available to those individuals who find themselves unemployed through no fault of their own. Refusing an interview for suitable work would render someone unemployed "through fault," since by their voluntary actions they are remaining unemployed.
The question in your wife's case is whether the job she would be interviewing for is a job offer of "suitable" work. Suitable work is work that is roughly comparable to the individual's previous work in terms of job responsibilities and pay. It does not mean that the job must pay exactly the same amount.
The precise threshold for how much "less" the new job must pay in order for a refusal to interview not to result in disqualification from benefits is unclear. A rough rule of thumb is 30%, but ultimately this is judged by the unemployment office on a case by case basis. More importantly, though, at this point your wife does not know how much the new job would pay. So, she really can't refuse the job interview on the ground that it is not an offer of suitable work because she does not know enough about the new job to say that.
Putting this all together, your wife would almost certainly need to interview in order to maintain her eligibility for benefits. If she is offered the job and she does not believe it is an offer of "suitable work" once the terms have been revealed to her, she could decline the position at that time and most likely retain eligibility for benefits. The caveat is that unemployment benefit eligibility is always judged on a case by case basis, so there are never any guarantees when you refuse an offer of work. Also, you definitely want to make sure to get the new proposed terms of employment in writing, that way the employer can't lie and say that they were offering better terms than what were refused.
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