Both the plastic cards and the paper cards have "ticket code" written on them.
The Plastic cards have two numbers, the top number is your Ticket ID#. That number can be decoded to indicate a specific ticket via where it was printed, which day it was printed, and the ticket # printed at that station that day. I usually need to have a "cheat sheet" to tell the location - but past that it's fairly easy.
The paper cards are a little easier to decode. They have a 3 letter and 3 number code to tell you the location it was printed, then the date, then the ticket number of that station for the day. It can easily be read at a glance.
These numbers are used as back-up in case the magnetic strip should become demagnitized.
If you are staying on site, the tickets linked to your room card are saved in the computer. I beleive they only stay in the computer "live" for about a week after you end your stay. After that, I'm not sure if it can be pulled up via name or not.
Paper tickets can only be pulled up via the code on the back of the ticket. Sometimes if you do will-call, and pick them up - the tickets can be traced back that way. The tickets can also be traced back via the receipt you receive from Disney, as it shows the specific transaction you bought them on.
Should you buy tickets from online sources, you do not recieve disney's receipt with the transaction codes on them. The only way you can protect yourself is to photocopy the back of the tickets. If you don't - and you lose them, it's just like losing cash. The only way those tickets are linked to anyone would be the transaction that (Insert online seller's name ) bought them, and it could be one of 1,000 tickets in a single transaction.