All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.

The right over which a long period of time has passed and whose holder hadn`t claimed it from the person liable for it, or what contemporary jurists have called "Expiry of a right through the passage of time," is: "When a specific period of time passes over a right or a property, for which someone is liable, without being claimed by the person to whom it belongs although he/she is able to claim it." {Al-Madkhal Al-Fiqhi Al-`Aam, V.1:243}. 

Legally speaking, these cases do expire through the passage of time; however, according to Sharia, they don`t expire because no one has the right to take someone`s wealth without a legitimate excuse and also because a right is eternal and doesn`t expire save through an acceptable excuse from Sharia. And Allah the Almighty knows best.