Some visas are dual intent (Hs) - ie planning to remain permanently in the US is acceptable - while others (Fs, Js and Bs) would not be granted to someone who did not intend to return to their home country at the end of their authorized stay in the US. It is a problem on reentry on the Fs, Js, and Bs if it appears that one is planning to or has filed for a green card.
Since you appear to be having difficulty understanding the issues with her status, I suggest you consult an attorney for assistance in formulating a plan. You need to be prepared to support her without her having a job indefinitely since I do not believe you understand the issues in university hiring of visiting scholars verses permanent staff members.

