How did the Israelites who were incredibly rich lose their wealth to the Egyptians?

Answer 1

They did not, they originally descended to Egypt out of poverty and hunger.

See more details below:

Israel, (the second name of Jacob) and the name of the nation, descended to Egypt (physically and spiritually) to reunite with his lost son Josef who became the Pharaoh's right hand after the really well hunger crisis management by understanding Pharaoh's dream and acting accordingly .

Josef and his brothers found each other again because there was hunger in the "Land" of Israel and the brothers came to Egypt to ask to food, so they didn't came rich to Egypt. Neither they became rich there.

Despite the fact that Josef was the savior of Egypt and of the entire ancient world, Egyptians did not remembered it for too long and a new king who did not knew Josef came upon Egypt.

Israel (as a nation) who was originally settled outside the Egyptian population in a different spot called Goshen Land (the first Ghetto, by Jacob request) , started to mix with Egyptians.

This separation was intentionally made by Jacob in order to keep Israel from mixing up with Egypt and keep practicing their beliefs without being attempted by the Egyptian blasphemy and spiritual/actual impurity.

Mixing with other nations means embracing their blasphemous habits, mixed marriages, abandoning the original beliefs and practices , basically everything (beside their language and clothing) means the end of Israel. So God kept his covenant with Abraham by not letting it happen.

It is known that Israel went down 49 out of the possible 50 gates of spiritual impurity by mixing with the Egyptians. One more step would mean God resets the Creation because it has no option of any valid future.

Therefor God "injects" vitality again in this failing apparatus by changing the Egyptian elite's hearths to hate Israel in order to separate them. So they start practicing hate by killing every male born, enslave them and so on.

BTW, they also did it because the Egyptian Prophets knew that Israel's "savior" which will also over throne Pharaoh is about to be born. And so it was, his name was Moshe and he lived under Pharaoh's nose, ironically raised as a prince and leader by the Egyptians themselves.

Answer 2

Through the passing of time. Pharaohs died and new ones came along, less familiar and friendly to them.

Their prosperity, also, in Egypt in everything these "foreigners" did became a cause for "jealousy" among the Egyptians.

Also the Israelites grew in such numbers that a great fear of them arose.

"...the children of Israel were fruitful, and increased abundantly, and multiplied, and waxed exceeding mighty; and the land was filled with them.

"Now there rose up a new king [pharaoh] over Egypt, which knew not Joseph.

"And he said unto his people, Behold, the people of the children of Israel are more and mightier than we: Come on, let us deal wisely with them; lest they multiply, and it come to pass, that, when there falleth out any war, they join also unto our enemies, and fight against us, and so get them up out of the land.

"Therefore they did set over them taskmasters to afflict them with their burdens. And they built for Pharaoh treasure cities, Pithom and Raamses. But the more they afflicted them, the more they multiplied and grew. And they were grieved because of the children of Israel." (Ex.1:7-12)

And so it went.