Codes with the \emph{Identifiable Parent Property} (IPP) have been studied in the context of traitor tracing; such codes can be used to enable a data supplier to determine the origin of pirated data. We consider an analogous property for a set of binary strings $S$: if a new string $\tau$ is formed by concatenating substrings of members of $S$, we should be able to identify at least one original string which must have been used to generate $\tau$. We prove upper and lower bounds for the size of sets which satisfy this property