Slope fields and Euler’s method practice question 4

Along the solution, $\dfrac{dy}{dx}$ has the sign of $(x - 1)(y + 1)$. Starting at $y = 1$, can the solution ever reach the line $y = -1$, where every segment is flat?

The horizontal line $y = -1$ is itself a solution, so the solution through $(0, 1)$ stays above it and $y + 1 > 0$. Which factor then decides the sign of $\dfrac{dy}{dx}$?