“Ashur which is now Assyria.”
Excuse me for laughing, but Assyria hasn’t existed for about 2600 years. Ashur is simply Hebrew for Assyria.
This is a pretty simple question – the answer is in Tanach (or Wikipedia if you prefer). After Shlomo, there was a split into two kingdoms: Yehudah (which included Binyamin) and the Northern Kingdom of Yisrael (other 10 tribes). In about 722 BC the Kingdom of Ashur conquered the Kingdom of Yisrael and exiled the people. (This was late in the time of the Bayit Rishon). For the most part the exiled people were lost i.e. assimilated.
A number of years later Ashur fell to Bavel, who later conquered Yehudah and destroyed the Bet Hamikdash.
See Sefer Malachim (or Wikipedia) for more details.