Answer
Some of the descendants of the exiles from the northern kingdom returned to the land with the Judahites during the restoration in 538 B.C. Some of these had lived in Jerusalem and had not gone into exile in Assyria, but had been exiled with the Judahites (cf. 1 Ch. 9:3). Many of the Israelites, however, remained in Assyria (cf. 1 Ch. 5:26). There were also the Levites (e.g., Ezra 1:5; Neh. 11:20), who had inhabited both the northern and southern kingdoms (see Josh. 21). Ezra described the returnees as "Israel" not because Judah was considered to be the remnant of all the tribes, but because the returnees constituted a reunited kingdom that included descendants from both the northern and southern kingdoms (Ezra 2:2,59; 3:1). It is also worth noting that Persia controlled both Babylon and Assyria during this time (indeed, Cyrus was called the "king of Assyria"; see Ezra 6:22), so that Cyrus' edict in Ezra 1:2-4 also permitted the return of the northern tribes who still lived in Assyrian territories.
Answer by Ra McLaughlin
Ra McLaughlin is Vice President of Finance and Administration at Third Millennium Ministries.