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Spodoptera ornithogalli
On asparagus patch of country garden.
Unknown parasite on caterpillar.
I cannot help you much with the ID on the eggs cases. They are usually from a parasitic wasp or fly. If you really want to know the best way is to put the caterpillar in a jar and feed it well and see what hatches - fly or wasp. If you do not do that leave the caterpillar alive so that the beneficial fly or wasp can be born. They are the good guys and army worms not usually appreciated.