I wouldn't be that interested in that Hosta to bother digging since I get PI so easily. They're so easy to find inexpensively about anywhere plants are sold, but it sounds like you have more than one and that the cultivated area is not just the area in the pic. I would smother everything (with cardboard, not plastic) in the pic & start over next spring. But if there is someone willing to dig out the Hostas & the other plant that looks like Platycodon, they're definitely worth saving. Just ask them to gently shake the dirt off of the roots, then replant elsewhere right away. Then watch closely for sprouts since seeds could be lodged in them. And sprouts of anything else you did not plant. Grass, PI, other weeds can take over so easily if you are not paying attention often & pulling anything but your desirable plants. Mulch also helps cut-down on the amount of unwanted sprouts of any type.
Starting a garden by smothering & waiting until the next year to use is how I've always started, except a few areas where I live now. Big mistake I'll never make again, will always smother first in the future.