Before revision:  It is  shown that, for any incomplete market model from a wide class of models, there exists a complete market model with an arbitrarily close paths of the stock prices.
After revision:  It is well known that market completeness is not a robust property: a complete market model can be made incomplete via small random deviations of the coefficients. The paper shows that market incompleteness is also non-robust: small deviations can convert an incomplete model into a complete one. More precisely, it is shown that, for any incomplete market model from a wide class of models, there exists a complete market model with an arbitrarily close paths of the stock prices.