The small rubber lining might have been thrown away by one of my roommates
You need the rubber seal to make the instrument airtight, it won’t work without it.
You can make one quite simply out of leather if you have the tools. You’ll need a long ruler and a craft knife. You can buy a leather skirt or trousers from a charity shop and use that.
Or if you want to buy a replacement in the US, phone 888-892-6242 (option #1)
Part number: W4130341 (FRAME PACKING P-37D)