Apart from rare lone sickly   wolf attacking people. I haven't heard of a wolves killing a person here in my 20 something years living here. Wolves however tend to attack herd quite frequently. They're pretty satiated by it. Wolves are no big deal,
Now bears on the other hand seemed to attract some news highlight with the fire in Siberia. Last year there was a great wild fire in Siberia. Numerous bears migrated to Mongolian forests for food and lair. With the scarcity of food, there was reported case of bear attack on herders. But that's just last year. Before that, I haven't heard any bear attacks. We do have good animal control, heard they shot the bear who attacked the herders.
And that happened in Forest regions. The steppe, Gobi, Altai are all safe from animal attack. It might take a while for you to encounter any animal in the Gobi.
Lots of foreigners go for trips and I see no problems.
I looked at your other post and I know a couple of foreigners who live quite comfortably as farmers in Mongolia. Mainly vegetables and wheat. Mongolians are nomadic herders so farming culture is not as developed. There's lots of fertile land for farms. The infrastructure is developing rapidly. So this might be one of the last chance before Mongolia becomes not so Barren, not so unploughed.