If the coil is located on the back of the zipper instead of the front it is an Invisible Zipper. Metal zippers consist of individual metal teeth. They are typically made from nickel, brass, aluminum and manganese.
Cost of Repair. The cost to re-line a chimney can be very expensive! Repair costs generally range from about $2000.00 to $4500.00 per flue or more! In a Real Estate transaction, you may have the opportunity to negotiate defects that are disclosed as part of the inspection process.
Otherwise, if furnace flue is being abandoned because no longer needed, I would require the top be removed and replaced with a domed galvanized metal cap to keep insects and maybe rodents from taking up residence or using it as a nut cache - cost probably about $50-75 additional.