Have you taken out the bulbs and looked at them? Honestly, I think the simplest solution's the best here...CHANGE THE HEADLIGHT BULBS! What you described sounds a typical headlight burnout. If you don't believe me, take the bulb out and look for any black marks on the glass, and check the filament. That's a little coil of wire which makes the lights turn on...usually they're between two posts, and if the light's burnt out, the filament will be lying on the bottom of the glass or hanging off one of the posts...but this isn't always the case, which is why you should change them with brand new bulbs no matter what!
The reason her high beams went out (and I'm sure everyone coming at her REALLY appreciated that) was that they're designed to run hotter and for shorter periods of time. They won't last as long if you leave them on full bore all the time. And people get really pissed at you if you do that. Not to mention, it's illegal and dangerous to blind oncoming traffic! As well, the high-beam filament can get damaged when the low-beam lamps go out, as some remnants can sometimes short out the high-beam filament. And, sometimes the low-beam filament isn't entirely dead when the lights go out, and they can flash one more time just before they give up the ghost for good.
Now, if you'd said that you had just changed the bulbs and this happened, I'd say that your assumption of a resistor or ballast might be right. But don't go assuming worst-case scenario when it could be as cheap as a trip to your local AutoZone for some new Sylvanias!
But, hey, if you wanna take it to your mechanic, I'm sure he'll love to check the resistors...and then change the bulbs anyway! Ballasts and resistors are usually pretty rugged, especially resistors, which are coils of high-resistance wire in a ceramic casing. If you've actually burned out one of those, that might be a sign you have other problems, like a short. But, yeah, this is a case where you do the cheap fix first, and THEN do the expensive fix if it doesn't work! Those are good cases!