Question about liriope

I have a number of variegated liriope in my front yard planting beds that never completely died back this year because we had a mild winter. Tiny new blades are emerging from the center of the plants, but the outer blades have dry ragged edges and just look limp and tired. Should I cut the plants back to the ground to let the new growth take over, or just cut off the ragged tips, maybe down one or two inches? TIA for any info.
Rhonda Richmond, VA USDA Zone 7
******** Basic human psychology is one of my subroutines.
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Chop 'em back if you don't mind the look. Liriope is very hard to kill.I thin mine out with a heavy metal rake and rip them up by the roots to get the dead off. It comes back green and happy.
Do you know anything about pond building? the Pond chat group is talking about Jesus or something. (I don't recall Jesus having a pond, so I think maybe their conversation is pretty worthless to me).
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