When Jacob learned that Joseph is the ruler over Egypt, he accepted Joseph’s offer and moved with his entire family to reside there. So began the Egyptian exile, which God had decreed many years earlier. The arrival of Jacob’s family in Egypt was inevitable in any case, but God eased the manner in which it transpired.

This can be compared to a cow that people were pulling to the slaughterhouse, but it would not allow itself to be pulled. What did they do to it? They pulled its offspring in front of it, and the mother cow followed after it against its will, involuntarily. So too, it would have been fitting for Jacob our patriarch to descend to Egypt even in body chains and in neck chains [i.e., by force]. The Holy One, blessed be He, said: Will I take my firstborn son Jacob down in shame? And if I place the idea to bring Jacob to Egypt in Pharaoh’s heart, [that may be carried out in a way that is distasteful to Jacob]. I will not take him down publicly. Rather, I will draw his son before him, and Jacob will descend after him against his will, involuntarily. (Bereshit Rabba 86)