IrisLily,
Here is an older thread that might shed some light on the stray plants. There are still registered plants that have that trate of sending out rhizomes "runners".
The thread "Rhizomatous daylilies?" in
Daylilies forum
Here are a couple of photos I took a few years ago, I had a few cultivars that still processed this trait.
I think this is actually a rhizome, the mulch I think was so thick it was acting as soil. So this "runner" would have been a rhizome I think even though it was on top of the soil, but under the mulch. I used to call them stolons, but I was told stolons run on top of the soil and rhizomes run below the soil level.