I've got a weird question. Assume that you have a small sample where the dependent variable that you're going to analyze with a simple linear model is highly left skewed. Thus you assume that $u$ is not normally distributed, because this would result in normally distributed $y$. But when you compute the QQ-Normal plot there is evidence, that the residuals are normally distributed. Thus anyone can assume that the error term is normally distributed, although $y$ is not. So what does it mean, when the error term seems to be normally distributed, but $y$ does not?
It is reasonable for the residuals in a regression problem to be normally distributed, even though the response variable is not.  Consider a univariate regression problem where $y \sim \mathcal{N}(\beta x, \sigma^2)$. so that the regression model is appropriate, and further assume that the true value of $\beta=1$.  In this case, while the residuals of the true regression model are normal, the distribution of $y$ depends on the distribution of $x$, as the conditional mean of $y$ is a function of $x$.  If the dataset has a lot of values of $x$ that are close to zero and progressively fewer the higher the value of $x$, then the distribution of $y$ will be skewed to the right.  If values of $x$ are distributed symmetrically, then $y$ will be distributed symmetrically, and so forth.  For a regression problem, we only assume that the response is normal conditioned on the value of $x$.