Live ones make great house pets, climbing up walls, curtains , etc. Try putting it by a saucer of weed leaves to eat. Put some tinsel out for it to put on its case.
Probably parasitised, or a female. The female stays in the cocoon, and is fertised by a male pushing the prehensile tip of his abdomen through the anal hole in the case. Try cutting the case open, carefully with say nail scissors, and see if there is an inmate. Could be remains of parasitic wasp cocoons in there, or empty pupal skin of a male, or live or mummified female.
Read the reference attached to the metura elongatus identification. Answered my question being, how did they get out of that tiny exit without ruining the cocoon. The mature male looks very strange and very fabulous.
Neuroptera, to my knowledge - do not have spurs on their legs (shot2, 4) - (except for dustywings - Coniopterygidae, which this is not) have translucent wings - don't have square ended wings (shot1) - have long 'neck' thorax with wings attached some distance from head https://inaturalist.ala.org.au/observations?place_id=6744&taxon_id=48763&view=species