They didn't.
There are no records of any Israelites being in Egypt apart from the Old Testament.
No Egyptian records or any other records mention them at all.
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The number of Israelites that did not leave Egypt is not mentioned in the Old Testament. It is estimated about 2 million to 3 million did leave Egypt, including men, women and children.
The Gibeonites were slaves by choice at least when the book of Joshua was written. Joshua 9:27. They were still under Israel's promise by 2 Samuel21:1-14, and had to be avenged. We see them come back out of Israel's Captivity in Nehemiah 7:25, presumably not as slaves any longer, probably having mixed in with the Israelites.
According to the Biblical narrative, the Israelites approached Palestine from the East (where Jordan is now). According to archaeology, the Israelites were endemic to the Judean Highlands of Palestine (in what is now the West Bank and central Israel).
The first Jew, Abraham came from Canaan (now Israel). Jews then were in Egypt as slaves during the reign of Ramses. Moses 'delivered' the Israellites and lead the Jews to a 40 year journey through the Sinai to Israel.
Every one in Egypt was affected, as frogs were everywhere, Not only the ones god sent but also the ones the Egyptian magcians made to come on the land. magi