Is there any case that changed from earthquake safe zone to danger zone? As plates move, I think that earthquakes belt will change over time. But is there really a case in which the earthquake-safe zone was replaced by an earthquake-prone region for such a shift or for any other reason? Or is there a region that is predicted to be an earthquake hazard zone in the future?
Yes, prior to 1983, central Idaho was classified low to moderate. On October 28, 1983, a powerful earthquake occurred in Lost River Range at Borah Peak in central Idaho. The shock measured 6.9 on the moment magnitude scale and had a maximum Mercalli intensity of IX (Violent).
The earthquake was centered only 50 miles from a Idaho National Engineering Lab (nuclear research laboratory), but no damage was reported a the site.
Unfortunately, I can't find an internet accessible report but I remember discussing this earthquake at length in a Engineering Geology class I was taking in 1986. The magnitude of the Borah Peak surprised the US government prompted the USGS to reclassify earthquake hazard zones in Idaho and Utah.
Current quake hazard map (from USGS:)
Yes, for example, earthquakes have increased dramatically in Oklahoma since 2009 due to the effects of hydraulic fracking; this has sometimes been nicknamed the Oklahoma Earthquake Swarm.
Link for Oklahoma Area Seismicity from 1973-2016: https://earthquake.usgs.gov/earthquakes/byregion/oklahoma/OKquakes1973_062642016v3.pdf
Link for USGS Hazard Estimation for induced earthquakes: https://earthquake.usgs.gov/research/induced/hazards.php
The first link provides a good view for how the history of earthquakes in Oklahoma. The second provides data of past and predicted hazards of induced earthquakes (earthquakes caused by human activity rather than natural plate movement) in the US.