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Looks like tradescantia pallida....

I believe it is Tradescantia pallida. If so terribly invasive.

OCwormgirl is correct. Tradescantia pallida, aka setcreasea pallida, or setcreasea purpurea, is a hardy, vigorous groundcover where you want it. It has recently become increasingly common in drought-tolerant plantings in highway median strips. Unfortunately, it is also a hardy, vigorous groundcover where you don't want it. And it has a mind of its own as to where it spreads.
Since your "almost mine" home in not yet fully yours, I would certainly have your real estate agent take up the matter with the sellers. It is likely that you can compel them to eradicate this plant before closing, the same as if it were termites or vermin. Don't let anyone tell you it's no big deal. (Remember that the sellers, their agent, and even your agent have every reason--$$-to downplay this.) The fact that it is at your foundation is especially concerning. Good luck.

Kay

Thanks for the feedback - unfortunately, I'm already 100% committed to the property (I take possession this week and all contingencies have been lifted). Hoping I can get in under the house right away and do everything I can to eradicate it from the foundation area, but I've read many horror stories in the last few hours.

If anyone has any suggestions for how best to attack it, I'm all ears... The sad thing is that it's a beautiful plant that would look great in the back yard!

You can try the Dandelion Treatment: fill a spray bottle with white vinegar and give each sprout a strong squirt, more than once if necessary. (Some people boil the white vinegar down a bit to concentrate it more, and use it while it's still hot.) If you do, use caution (aka gloves), because the vinegar can be a lot more acidic that way.

Vinegar is probably the most environmentally benign way to try to get rid of it. Hopefully it will both kill the top and make the roots shrivel. That said, I must confess I haven't tried to eradicate this particular plant that way.

Kay

Thanks - it's worth a shot! Vinegar's an easy approach for a novice like myself to take, and I'd rather not have to go to drastic extremes that would compromise the soil or other plants.

While I'd normally go with the vinegar, this time I'd go with RoundUp, especially around the foundation and stone walls, because this will also kill the roots and not just the tops.

Stuff won't grow for me. When I plant it, it lasts for a couple seasons then dies out. I think it gets too hot here and I'm not very good about watering consistently. The occasional deep watering I give my trees and shrubs isn't enough for it.

Try "horticultural vinegar" available on Amazon.

If no joy with that, I'd go with glyphosate.

Here is a link that might be useful: on amazon

Horticultural vinegar. . . who knew?
Thanks, evilscott, for linking to a product I had no idea existed. And of course, now that I know about it, I have to add it to the anti-weed arsenal. The vinegun (what my DH calls the spray bottle I fill with vinegar to use on dandelions--and indeed on anything that has the audacity to try growing between the pavers in the driveway) will be filled with high-test from now on!

Kay