If it gets too complicated, you could take it to an alterations shop to see if they can put it back together for you 
I’ve done a lot of sewing, but I’m not very confident when it comes to lingerie! I was prepared to alter a teddy I ordered if it didn’t fit because I really liked it, but it fit, so I didn’t have to! The only LH item I’ve “repaired” was this wand storage bag 
Like @Baby_Jane said, you can google different stitches or do a search on YouTube to find a good video tutorial like these, How to Sew with Elastic Thread on a Sewing Machine and Zigzag Stitch for Sewing Elastic. Hope you can salvage it 
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