Hyatt didn't use to enforce expiration. Starting in 1/1/14 they do.

I have had no activity in way way more than that, over 5 years, and they recently sent me an email that if I didn't have activity in the coming months, my account would closed (I forget on which exact date).

But the point is the Hyatt expiration is now 2 years. That doesn't mean they have to expire points after 2 years, just that they can. In any program, if you find you've not activity for longer than the expiration time listed here, don't assume that you're some exception that can go on that way forever, assume instead that have some undocumented limited grace period, but since you don't what this, assume that you may be facing expiration the very next day, and try to get some activity happening ASAP.

If you want to delve deeper into whether it's safe to wait until 1/1/16, or whether your wife should create some activity tonight, that would be more suited for the Hyatt forum that this thread. This thread is intended as a summary, not a deep examination of the complexities of each program's policies (and changes in such policies). Most importantly, it presumably takes Hyatt experts to answer your question, but there are way more Hyatt experts in the Hyatt forum than likely to visit this thread in MilesBuzz! soon.