This sounds more like a moth larvae, and they will encase themselves in silk where they morph into adult moths. Bugs,even spiders can be fascinating if you take the time to observe them.

My aunt keeps caterpillars for pets, and they make silk cocoons and morph into butterflies.

I don't think so. Could it have been a beetle that got caught in a spider's web?

Just saw something unusual: an insect that looked like a thin black beetle about 10mm long, hanging by a thread from the ceiling. The underside of it seemed to be covered in white fluff and it was busy doing something with its front legs, almost like a spider wrapping up a fly, but it was definitely not a spider.

Using its thread I moved it to a hedge in the garden. That didn't seem to disturb it. I had to leave then so I didn't see what it did next.

I'm intrigued. Any suggestions as to what was going on? This was in North west England by the way.