This is not entirely unusual for Snake Plants, which can form stolons (creeping stems that produce new clumps of leaves) as they mature. While there are many varieties of Snake Plant on the market these days, the pictured plant looks less vigorous and thick-leaved than it should be, which suggests that it might not be getting enough light. Snake Plant has a reputation for tolerating low light, but they do not thrive in those conditions, and need moderately bright light to do well over the long term and keep the leaves compact, dense, and sturdy. If the plant isn't close to a window with some sun or bright-indirect light, you can try putting it closer, or using a grow light to supplement what it's getting naturally. Ambient room light is not enough, including for low-light plants, even though it can take a while for slow-growing species like this to show signs of decline.

For now, aside from possibly moving the plant into brighter light, just make sure the roots don't stay too damp, since repotting into larger containers can make it easier to accidentally over-water plants that don't have enough root mass to fill the container yet. Fortunately, Snake Plant does well when the potting mix dries out between waterings. There is no need to trim off the stolons (and they are probably too stiff to nudge down into the potting mix without snapping, or too stiff to stay there unless held down by something sturdy), but if you don't like the look of them, they will probably become less obvious as the plant fills in.

Miri

Thank you very much for the detailed response.  I have two of these plants and have moved them closer to sunlight.  I will try to get them better exposure.
I will mind the watering.  I know that in some cases I am a chronic over-waterer.  I will reduce my watering from once a week and monitor their health.
Regards, Mitchell

Mitchell Solkowitz
(he/him/his)

You're welcome.

When plants are repotted, the soil level should stay the same -- no shallower, no deeper -- so the roots are not stressed by a change in soil depth. (Too deep and it could affect how much oxygen they can get, and too shallow could dry them out faster.) We do not recommend adding more soil to the Snake Plant's pot unless you know you potted it shallowly compared to how it was growing before. The stolons are probably not flexible enough to tuck them into the soil, and they do not need to be buried (rhizomes are underground runners, stolons are above-ground runners).

Miri