Generic subsets of partially ordered sets play an important role in giving significant examples of Zermelo-Fraenkel set-theoretical models. The significance of these models lies in the fact that a generic subset $G$ of a partially ordered set $P$, in general, does not exist in a model $M$ in which $P$ exists. Thus, by adjoining $G$ to $M$ an interesting extended model may ensue which has properties not shared by $M$. Thus, in considering generic extensions of set-theoretical models it is quite relevant to know whether or not a generic subset of a partially ordered set $P$ exists in the same model in which $P$ exists. In this paper, we give a necessary and sufficient condition for $P$ to have a generic subset in the same model.