I grow horseradish in three places in the garden where the earth is really rich and the big roots are worth harvesting. If it's not getting enough nutriments it wears itself out but it will stay alive and take up space without giving anything back. You don't need much to get enough sauce for a year.
Once your plants are really showing signs of enjoying life and have huge healthy leaves, then wait until the end of summer when they start to wither, then dig straight down around the plant with a spade, wiggle it a bit to get the whole complete root out. You can then decide to leave some in for next year or to take the whole lot out. It's only when you cut the root in little bits that it becomes invasive.
Here, it's growing next to Egyptian onions, Melissa, Rhubarb and some pink Lamium.