Some families had the money and wisdom to leave - friends of mine's grandfather removed his family from Poland prior to Hitler's invasion.
Expect that many remained in denial as to where things were going - human nature, and many just didn't have the money, as I expect in those days, that transportation out of Europe would have been expensive; plus leaving their homes and businesses possibly unsold or sold for pennies in the Deutschmark or whatever currency applied probably went against the grain. Many people would find it innately difficult to just walk away with only the proverbial clothes on their backs and a little money in hand.
At the same time they would not have been classified as refugees... did the understanding of the term and protections in law even exist then? I don't think so. Therefore they were at the mercy of whichever country they applied to for entry.
