Do Jews have a home?
There is the current country of Israel where any Jew from around the word can naturalize as a citizen.
It depends on the exile in question. Most Jews that wanted to returned to Land of Israel after the exile in Babylonia on account of Cyrus the Great. Many Jews have returned to Israel in the last 150 years from the Roman Exiling of the Jews nearly 2000 years ago. However, not all Jews have returned home after exile in both cases.