Answer: This is not a woody plant or shrub but rather an herbaceous perennial, meaning it dies back to the ground each winter.
The old stems should be removed at some point once they have been frozen back, it can be done in either fall or spring, for sanitation purposes. Trimming off just the spent flowers (deadheading) promptly in fall will prevent the plant from reseeding; however some gardeners feel they add winter interest and so leave them until spring.
Next spring, be very patient in waiting for the plant to come up--it usually gets a late start and you won't see new shoots until long after your other perennials have begun growing. You might want to mark its location to avoid stepping on it or planting something else on top of it by accident while you are waiting.
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