The phase structure of strongly interacting matter is a central topic in high-energy nuclear collisions and the search for a first-order phase transition between the quark-gluon plasma and the hadronic gas presents a particular challenge. We have explored the possibility that the expanding quark-gluon plasma breaks up into separate blobs prior to the hadronic freezeout, as it would be expected to do (via spinodal phase decomposition) if a first-order phase transition were encountered. If such a separation were to occur, the strangeness in a given blob would remain trapped during its further evolution and constrain its subsequent hadronization. For a broad range of freeze-out scenarios, we have studied this trapping mechanism and find that the strange-particle multiplicity fluctuations are significantly enhanced. Thus, the systematic measurement of kaon multiplicity fluctuations might offer an experimental means for elucidating the hadronization dynamics.