Not moving when I saw them. The one in the last photo has not moved for days - the flowers close at night but the next day there it is still in the same spot. There are currently 5 similar things on these daisies in our home garden; one of them (not in these photos) looks quite silky.
I dissected several shelters, including the one in the third photo which was I think old, and not silky, but no residents were found. Posting one photo of a newer silkier shelter showing what appears to be cut off parts of florets incorporated into the silk structure. Will look out for new shelters.
Terrific. A lot of caterpillar species web leaves together to make a shelter, but this the first I have seen webbing on a flower. It would be really interesting to find out more about it.