Some consequences of the strong interactions between K-particles and nucleons are discussed. A connection is noted between the associated production mechanism and spatial exchange characteristics of K-nucleon scattering. (The same is true for Λ0-nucleon scattering.) The K-nucleon interactions may possibly lead to bound states of K-particles in nuclear matter ("K-fragments"). If a θ0 fragment exists, its decay modes are 2-, 1-, or 0-mesonic. It is estimated that the former two modes would have comparable probabilities, while the last one is less probable by a factor ~0.005 if the spin of the θ0 is zero, or by a factor ~0.05 if the spin is 1. The results may have bearing on the interpretation of fragments with energy release larger than corresponds to a bound Λ0.