This paper introduces the notion of cache-tapping into information theoretic models of coded caching. In particular, the wiretap II model with two receivers equipped with fixed-size cache memories is considered. The adversary chooses a set of symbols from cache placement, delivery, or both to tap into. The legitimate parties know neither whether cache placement, delivery, or both transmissions are tapped, nor the positions of tapped symbols. Only the size of overall tapped set is known. The strong secrecy capacity, i.e., the maximum achievable file rate while keeping the overall library strongly secure, is identified for the instance of two library files. Achievability is established using a code design which combines wiretap coding, security embedding codes, one-time pad keys, and coded caching. The study overall demonstrates that information theoretic security guarantees are possible against a powerful adversary which optimizes its attack over both phases of a cache-aided communication system.