The photos are not clear enough or with sufficient detail to determine ID. Can you take a photo showing the entire planting? Has there been any signs of flowering?

FWIW, "groundcovers" that spring up spontaneously or that volunteer in the garden tend not to be real groundcovers at all but rather weeds with just a low growing, spreading habit. Just saying...........:-)

reminds me of portulaca, but don't know if that grows in Boston. Not evil or damaging to other plants. portulaca has yellow flowers and fancy hybrids which you get at nurseries come in all showy colors.

Hi gardengal48 and bossyvossy, and thank you both for speedy responses. I am not terribly optimistic that this is something I will want growing in my yard, but I am hoping against hope! After several years in this house, I finally gave up on the front part of our lawn, and as soon as the grass began to die down, we had some sedum pop up that looks great and is filling in really nicely. I had been pulling it not knowing what it was for six years and finally looked it up. So maybe there's a chance for this, too? At any rate, I pulled up a plant and tried to take a photo. First photo is this stuff growing in my brown yard. Second one is a closeup. My fingertip is in it for sizing perspective. Thanks again!

Hi - also, no flowers yet.