Capacitors are covered with a plastic sleeve which is only for the graphics and there is no difference in the performance of the capacitor if it is ripped as long as the aluminium can is not pierced. It would not be recommended to use a cap with a can which is not airtight.
The sleeves used to be Polyvinyl Chloride (PVC) but since the european RoHS directive they are now Polyethylene terephthalate (PET). Nichicon HD series have no sleeves and are promoted as being more environmentally friendly that way.
An aluminium can forms the capacitor casing and at the bottom is a rubber bung which is usually made from EPT Ethylene-Propylene Terpolymer which is a synthetic rubber. The can is crimped around the rubber bung forming an airtight seal.
Inside the capacitor are two strips of aluminium foil. One lead is crimped onto each of these foils. Then the foils are separated with a thin material which is soaked in electrolyte. Another piece of material covers the outer foil to insulate it from the aluminium can.
Then the package is rolled up very tightly and sealed with a piece of tape. We will explain how it works electrically in another article.