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for the short part of the safety belt - I think ? when you move the seat back- or forwards that this short part will keep in place
Actually, Turbo-joe is correct. That elastic part is a “keeper” for the seat belt buckle. As you can see from your photo, there is a snap on that leather covered elastic part and that snaps to a stud on the outer portion of the inside seat bolster. I personally don’t think it works very well in maintaining position of the seatbelt buckle, but that is what it is supposed to do.