Would help to know more about what she was trying to film.
Events (recitals, baseball games, weddings) where a long run time figures in may rule out some options.
Canon Vixia series or Panasonic TMCs both are pretty good in low light, but that $500 price limit will test that. You may want to look for a good used one, especially if she is just starting out. Get as much manual control as you can.
For more flexibility lens side, consider a Sony Nex5/6/7, but that will limit record times. You can get OIS lenses for the camcorders that use the same mounts, but they will get pricy fast. Get the 50mm/F1.8 and "zoom with your feet" for some pretty decent low-ish light work. Indoors, I use that lens on my VG-20 more than the 18-200 zoom.
Audio on all camcorders sucks. All of them. Even $5000 ones. The camcorder is generally a rotten place to have a microphone. Invest in an Audio recorder like the Zoom H2 or Olympus OM11 or equivalent. Get even a $15 lapel mike and drop the audio recorder in a pocket.
I have a Sony Nex VG-20 and a Nikon 7000 with a rode video mic. The best audio I get is off a lapel mike on the talent, and just use the audio from the camcorder to sync it up (which FCP X will do very easily for you most of the time).
So -
$15 lapel microphone (get a better one later as needed, plenty on amazon)
$80 personal audio recorder
(
http://www.amazon.com/TASCAM-DR-05-...=zoom+h2&pebp=1422315063233&peasin=B004OU2IQG ) I haven't used this one, but it should work.
Pretty much leaves her $400 for a camera since you said she wanted decent audio.
Now how much trouble does she want? The NEX 5 with a decent lens might squeeze under that budget in the used market, but will not be as easy as a Canon or Panasonic (at her price point, I like them better than JVC/Sony/anyone else).
She could get a Vixa RF5x. The sensor is kind of small, and few manual controls, but long record times. Then shoot b-roll with iphone 6 or similar to give her two angles once she uses a tripod or trains a sidekick.
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Don't Cannons have the IS on the body, and Nikons have it on the lens?
I do not think Optical Image stabilization is in the body. I believe it has to be in the lens because of how it works. I know the sell IS lenses, so not all canon's have it.
Anyway, a DSLR +decent lens would be a tough fit in a $500 budget requiring decent audio.