It is an interview question, I simplify the question as dim = 1, it is better if the solution is about multiple dimension.
We know that the assumption of OLS is
$$y = ax+b+\epsilon,\quad \epsilon\sim N(0,\sigma^2).$$
And its estimation is unbiased. Then if we change the assumption to
$$y = a(x+\epsilon)+b,\quad \epsilon\sim N(0,\sigma^2),$$
what's the bias of estimation?
It seems we should solve the estimation of $a,b$ by MLE first (replace $\sigma$ by $a\sigma$) and the solution is no longer equivalent to OLS solution, which is more complicate.