I don't know if you are aware that the northern kingdom was greatly weakened by a war with Syria. Syrian was also weakened. Then the Assyrians came in and first took out the Syrians. Next on the list were the weakend northerners and that's all she wrote.
Yes, and this came at a bad time. The split between the Kingdoms in 933 BC was not for nothing, and the North and South continued to battle. The first 80 years after the split was continuous warfare. The next 80 years was more or less peaceful. The final 50 years before the Assyrians took over there was intermittant war between the Kingdoms.
It was a time of constant stress, then came war with Syria on their north which lasted until 732 BC. Soon the Assyrians were on their border, and by 721 BC all traces of the Northern Kingdom were gone.
The Assyrians were at best simply encouraged by the South. At worst, they were substantially aided. To the extend the Assyrians were aided by the Southern Kingdom their job was simplified and their military needs were reduced.