Old tickets are good forever, for what they were bought for. If it was a hopper with plus options then it is still good for the days left. You can have it checked at a Disney hotel on check-in or at Guest Services. If the ticket is from last year then you don't have to do the finger scan. You can also upgrade the ticket when you buy the rest of the tickets that you need, but I don't recommend this. When you upgrade you only get the value of the ticket at the time it was purchased. If you use it for a day's admission then it's worth the days price, no matter what the price increase is.
Old tickets are not tied to one individuals finger scan, which is why Disney is now doing finger scans.