Lug nut covers [chrome caps]

That's a Ford Class C chassis, E450 or E350-DRW. I see the the hub studs called 9/16" and some metric size I forget. Anyhow, torque spec is 140-ft-lb. I agree with the idea that they were either over-torqued on assembly, OR possibly the nut got galled to the stud threads and the force it took to get it tightened down OR removed was enough to weaken the stud.

Replace Them! Studs AND whomever your Tire Tech is!

A couple tips:

Be sure the shop buys studs long enough to leave the few threads showing beyond the nut, to allow the wheel covers to be installed. It's been a long time, but we had an OP who bought new rotors with studs that worked till he went to put the simulators on, then found he had no threads to catch on to.

If you're going to pull the hub/rotor assembly to take to a shop, the Brake Caliper comes off very easily. Just pry it open a little (so the pads don't keep you from getting it off the rotor), and tie it up out of the way so there's no strain on the hose.

BUT the Caliper Bracket is torqued pretty high (150, 170 I forget exactly what) and I found I couldn't get them loose on a trip when I had brake trouble. It's 21mm but a 13/16" (or maybe a 7/8" again I forget since I bought a 21mm) will also work. But it takes a breaker bar to pop it loose. Besides the torque, the threads get rusty. I'm blessed with an old 3/4" drive socket set and its breaker bar gave me more leverage than 1/2" would, and without the flexing. Just be sure you have good tools ready, hopefully with a strong assistant!

Agree, the sheared stud is unrelated to the missing lug nut cap.

And, with only one lug nut missing (and 7 good ones), there was no danger of loosing a wheel. Now, if the remaining lug nuts were not properly torqued, THAT is another issue.

You need to get the sheared stud replaced and the others checked very carefully for signs of cracking, stretching or damaged threads.

From the pictures, the stud opposite the missing wheel cover thingy sheared off, so the lug nut and the wheel cover came off the wheel.

I don't think this is the fault of the wheel cover, nor of any imbalance caused by the missing nut. Broken studs in my limited experience usually results from overtorquing, either when installing the lug nuts or when trying to break the free after they've rusted together. There may well be other somewhat common causes. That one has broken does not particularly inspire confidence in the others, since presumably they've been through similar use and abuse.

Notice the valve stem placement.

https://www.facebook.com/photo.php?fbid=10205753354899576&set=a.10200116124412337.1073741828.1427209269&type=3&theater

https://www.facebook.com/photo.php?fbid=10205753355339587&set=a.10200116124412337.1073741828.1427209269&type=3&theater

A missing lug nut cover didn't cause you to almost lose a wheel. You had a lot bigger issue than a loose lug nut cover.
Even one loose lug nut won't cause a wheel to come off.

Sorry, but a lug nut cover (at least on 10 lug 22.5") weigh less than .10 ounce. No way would one throw balance off enough to cause an issue, much less loss of wheel.

Pictures or details PLEASE!

"Almost lost the front wheel" as in loose lug nuts????

My thoughts are that he had loose lug nuts that were not tight. The simulator had nothing to do with it or balance. He doesn't mention any vibration after leaving the shop. Loose nuts would cut simulator loose first as a warning. MOHO

On a previous MH two of the lug nut simulator fasteners (you call them covers) were used to hold on the simulator. You can run without one but the other must be tight! I did it for thousands of miles. I'll bet it wasn't a balance issue at all, just a loose simulator.