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Yes, I think this is fixable. Is this an old Zeagle by chance? Anyway, the top of the inflator hose has an elbow, sometimes with a valve. This elbow has a flange on the end that goes into the bladder and is typically glued to this polyurethane bladder opening you're showing. For glue you can use 3M Marine Adhesive Sealant, available at boat shops or online. You can use that to patch leaks in the bladder, too. Hope this helps!
Livewire, do you think the 3m marine adhesive you suggested would repair a cut in a safety sausage?