The lexica of natural languages are ambiguous, but the degree of ambiguity is unequal between words. Some words have more meanings than others. However, the exact properties that favor some words over others when acquiring a new meaning are not very well understood. In recent years, several studies suggested that some words gain more meanings than others based on selection for efficient communication, which could explain the correlation between meaning and frequency discovered by Zipf (Piantadosi, Tily, & Gibson, 2012; Gibson et al., 2019). The object of this study is to assess the role of selection in the meaning-frequency correlation using a neutral model that yields a meaning-frequency correlation without selection pressures. We provide a model where words gain additional meanings through reuse. In the neutral model presented in this paper, words are chosen to be reused at random, independently of their frequency, hence there is no selection mechanism favoring efficient communication. Unlike previous attempts to introduce null models of the meaning-frequency correlation (Caplan, Kodner, & Yang, 2020; Trott & Bergen, 2020), it truly does not rely on selection for frequency. We show that statistical regularities related to ambiguity, such as Zipf's meaning-frequency correlation, can arise in conditions when words are not undergoing any selective pressures. This model has the additional property of matching word frequency distributions of natural languages. It can provide the baseline against which the presence of selection for efficient communication in natural languages can be assessed.