I have a headcanon for what borrowers do, but the little guys in my stories, despite their resemblances, are not actual borrowers from the Mary Norton books. There are some differences, some that haven’t been revealed yet.
As for what my guys do with their dead in canon, we actually do touch on that in a few different stories. They don’t hold any religious beliefs themselves, so it depends on where they live. Each subgroup will handle it differently. The families living in the burrow behind Bobby’s have a place chosen beyond the tiny stream they live next to where they wrap and bury their dead. A tiny field of flowers grows overtop and if anyone misses their loved ones they can come and sit near the field and feel close to those they’ve lost.