Is it possible for the meniscus to simply wear away?

YES... That is simply the most common reason for people to have meniscal tears... Like your favorite pair of blue jeans... You feel a breeze one day and look down and see a hole... The fabric simply wore out with time... The same thing can happen with our menisci, rotator cuff, etc.
Not exactly. It is common for patients to experience degenerative meniscus tears as they age (often seen in patients 50 years and above). Thus, the meniscus can become fragmented, displaced and less functional. However, it rarely simply goes away.