My cats tear up most area rugs but never wall-to-wall carpet. I have no idea what difference they perceive.

You could get a look similar to sisal (minus the texture) with a flat-weave carpet in a similar color. I think I would choose some berber carpet and have a section bound. Ordinary rug binding is narrow and similar in color to the carpet, but it would be possible to have a wider, contrasting border.

I have two cats and neither goes after the wool rug I have that is looped like a sisal rug (it's the Karastan French Check). They are not perfect creatures, there are some textures they go after (the backing on the bathroom rug is one, the flip side of "Oriental" rugs is another). I believe my cats would go after actual sisal because they have those corrugated cardboard scratching pads, which they love, that are a similar texture.

Oh, just read the part about "digging up" any rug with a pile. Hmmm, I think it's a lost cause unless she can retrain them. Do they have scratching pads and/or towers? They need to scratch, if that energy isn't directed towards something you want scratched they will scratch whatever they want.

Varies drastically with the cat. Mine always ripped the living daylights out of berber and any other kind of looped floorcovering, and once they get a loop pulled out it makes a "run" just like nylons. Looks ghastly and we had to pay to replace the carpet in more than one apartment! She had scratching posts and pads and gizmos galore and completely ignored them for her entire life, preferring to tear up looped carpets/rugs and any carpet where she could get through to the backing easily, like on stairs where the carpet is bent over the 90 degree angle of the step. (She was also completely immune to catnip, which is most commonly used to attract cats to scratching paraphernalia.) But, she never went after furniture, which many cats just love to mangle, so it's impossible to say what cats are going to do to a surface they've never encountered before.

I'd start her off with a relatively inexpensive polypropylene/olefin faux sisal (often sold as indoor-outdoor rugs, but they're softer and better-looking than they sound) and if that goes over okay she can graduate up to a more expensive wool version if she wants, although I've been quite happy with the several olefin rugs I've had over the years. Or, she can visit a bunch of carpet dealers and see if she can get a remnant of faux sisal carpet bound, which can be a good bit cheaper than a readymade area rug, or get a small rug (like 2x3, which could then maybe function as a doormat somewhere) to see how they react to that particular texture before investing in a larger one.

My cats choose by price. The very expensive oriental rug in the living room would be their favorite if we didn't make it absolutely clear that we do not approve!
Actually, they will take a run at any of the rugs, but not with a lot of gusto, as they too prefer the corrugated pads. But the sample idea is a very good one.

My cats must have "beer taste" to match my "beer budget." The upstairs where I have builder grade wall-to-wall carpet they have shredded the carpet in the thresholds of rooms to which they were denied access. They leave the fake wall-to-wall berber in the basement alone, but pee on the $5 scatter rug from Ikea and the mat in one bathroom but not the other. Go figure.

I think Johnmari has a good idea about trying a small rug before committing to a large one. I might try that idea myself.

When I brought my house there was a berber rug that my cat had a field day with. We repaced our steps w/ an expensive wall to wall w/ tight weave (don't remember what kind, but was pricey) which has held up much better, he still scratches but holds up better. I also have an oriental rugs in my main rooms, family room and basement that hold up great. He doesn't bother with them. If he does stretch on them has never caused a problem because they are so thick. My cat has never bothered w hanging curtains or the furniture (but he does leave his fur behind, so we have leather now), since he always had a scratching post, but depending or the rug he will scratch. The only problem with these rugs are now that he is getting older (he is 15) he has lots of hair balls which do leave there mark on the rugs. We send them out to get professionally cleaned every 1 - 2 yrs. Dogs also come w/ problems as well as the kids. I wouldn't go to light on a good rug if your afraid of stains showing.