1) In general, "Uncle Sam" doesn't pay unemployment benefits. Unemployment is administered by the state, using taxes collected from employers, and as oldmanbutters stated those taxes go up based on your history of successful claims filed against you, so the employer does have some incentive not to fire your SO. When the federal government makes extended unemployment benefits available, those are reimbursed by the federal government, but that would not apply here.
2) Depending on your state, you can sometimes get benefits when you are moved from a full-time to part-time position (i.e. partial unemployment), but I don't know the exact requirements where you live. If your SO doesn't have an agreement from the employer to provide a certain number of hours, or a well-established history of receiving a certain number of hours, then this probably isn't an option.
As to your actual question, that's really impossible to know without knowing all of the applicable state and local laws. If you think it's worth it, I would talk to a lawyer about it. If the trip to Israel had any religious significance, you'd have a much better case.