I used plastic boarding cards today. A thru flight had an aircraft swap, and to identify which pax would be those thru passengers, we gave them the yellow plastic boarding cards. They can't board a flight with nothing... that wouldn't fly with the security people. So to give them something, we use the plastic boarding cards.
The cards are kept behind or near the gate podium. It's usually kept with all of the supplies like paper, fuel slips, etc.
My posts/replies are strictly my opinion and not that of any company, organization, or Southwest Airlines.