That happened over the course of a year and I don't think there was a massive (enough) run on tether while it was low, since it didn't stay at that price for very long. There just isn't as much activity when bitcoin is low which I think also works in tether's favor. I think they do have significant btc backing them, just no USD.

I actually wrote a comment about their dynamic two years ago when this happened.

https://news.ycombinator.com/item?id=18222578