I have 2 days on an old Park Hopper Pass that has not been used and wanted to know if my son could use the 2 days left on it, or does the last person that used it have to be the one to finish using it?
How old? If they are pre-finger ID, you should be fine. But then your son will imprint it and they will be his forever. The finger ID was at least 2005, maybe sooner.
The first person who used it is the only person permitted to continue using it.
For best results, it should not be used on a vacation of four or more days, otherwise the value you get out of it could be as little as six dollars total.
No special treatment (unless you consider normal use of a finger scanner as special treatment) is needed when using tickets that did not originally use finger scanners.