Is your parsley safe? If you buy it at places like Lowes, their herbs are sprayed to keep those pesky caterpillars from eating up the plants. They don't realize that people will actually buy plants with caterpillars on them.
Flies/wasp can lay eggs in the eggs would you believe and then that can cause them to die or they will go through their cycle and out of the chrysalis will come the wasp or fly--scary.
If your house is too cool, below 70 then the cycle will take longer, but it shouldn't kill them.
If you raise them outside you will need a container that prevents the flies from laying on them through the netting.
These enclosures will keep the flies from laying on them through the netting outside. They are predator proof.