Currently there is a wide array of boarding cards that arrive at the door. AC stock, other airline stock, OLCI printouts, mobile, etc. At virtually every station where there is bona fide AC staff, the boarding cards are kept intact.

At most contract-handled stations internationally and domestic stations handled by UA, only the stub is presented. In the case of UA, IIRC, the boarding pass is fed into a scanner, and the larger portion is retained - with the stub being returned to the customer. At foreign contracted stations, perhaps it's simply part of the reconciliation or local handling procedures.

Often I tear only the J/Class stubs for jacket/garment identification.