I've done this several times and it was different each time, so there are lots of variables (which airport, how busy the agent is, type of ticket and fare, even your FF status, whether they want to do you a favour or go by the book). Best case they issue a boarding pass on the spot, annotate your PNR and let you deal with the lost ticket later (presuming you are tight on time and have to catch that flight). Worst case you buy a full fare very expensive ticket for the flights that you must take, and deal with getting a refund later (how much of a refund varies with the airline, AA is amongst the best fwiw). Most common case is something in between. My impression is that this is one circumstance in which your past dealings with the airline count for quite a bit (many "lost" tickets are attempts to defraud the airline by various schemes).