Thanks for your question.

Without a picture of your sedum, it is difficult to make a good diagnosis. The webbing that you described is probably due to spider mites.  This webbing is much finer than spider webbing.   Another symptom of spider mites feeding is yellowing or stippling on the leaves.

Here are some steps you could take:

1). Spray the plant with a strong stream of water to knock off the mites. Pay special attention to the undersides of the leaves.

2). Remove and discard heavily infested or damaged parts of the plant.

3). Apply insecticidal soap to the plant, ensuring thorough coverage on both the tops and undersides of the leaves. This soap works by suffocating the mites. Repeat every 5-7 days until the infestation is under control.

4).  Use a horticultural oil, such as Neem oil, to smother the mites.  Apply in the early morning or late evening to avoid leaf burn and ensure good coverage.

Here is some further information about spider mites:

https://www.gardentech.com/blog/pest-id-and-prevention/spider-mites-tiny-bugs-that-cause-big-problems - :~:text=Plants with mite damage limited,soggy or too dried out.

https://www.weekand.com/home-garden/article/kill-mites-sedum-plant-18017560.php

Fortunately, spider mites usually do not pose a significant problem for sedum. Once the infestation is eliminated, the plant generally recovers.

Good luck. Thanks for consulting us.