No clue what the term is, but have you been to the High Line in NYC or seen any photos of it? The asters there are planted amounts low mounded/tufted grasses, similar to the conditions you'd see them in a field. Sporobolus heterolepsis (Prairie Dropseed, native, depending on where you are) is one which was used a lot.

I tried good plants to hide leggy perennials and found discussions of planting things to hide leggy perennials and also discussions of planting perennials in front of other leggy things.

Consider also companion plants to hide leggy.

Or short plants to hide leggy.

Or instead of leggy try a search that includes bare stems.

I don't know that any of these will get you a really high percentage of useful sites, but you will get a variety of useful things.

Have you tried searches that include asters or some of the other plants in your garden that have this problem?

I have a prairie garden where I find the ugly legs of New England Asters quite unacceptable. I have enough NE Asters elsewhere in my planting, so, early in the season, I simply break off the ones that grow near the border. They break off rather easy and the grasses fill in nicely.

Don't you think your search is contradictory to a native-focused front yard? How do they look in the wild, do they grow tall looking for light because of the density of neighboring plants, is your situation like that? I am not trying to be smart (it comes naturally) but I would look to nature to provide your answer.

Orgle, quite a few years ago I heard Fred McGourty, author of The Perennial Gardener, speak at the Atlanta Botanic Garden. He referred to plants like the ones you speak of, saying they had 'UGLY ANKLES'. One example I recall was Carolina Jasmine.