I've never seen a jumping spider eat its own web (although a jumping spider's web hammock is quite different from the silk used by or weavers), but twice I have seen them collect the webs of other spiders and create dirt wads with them. I assumed they were just cleaning up their territory. Jumpers seem to be averse to walking on the sticky trap-type webs of other spiders.

Infertile hybrids undergo cell division and are able to replicate their own cells; it is how they grow and heal wounds. Cellular reproduction does not necessarily mean generating offspring.

You couldn't consider infertile hybrids to be their own species because of their infertility, but that does not exclude them from qualifying as living things.