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Your requirement is still unclear what tool you want to trigger on Decativate event?
If you want to do something when your tool is not active tool use Neils tip.
If you want to do something when some other tool, that you don't implement in your extension you can just test if the tool is active and after that if is inactive. In ArcMap in ITool Enabled is invoked at least once a second.
Other way goes very low into hooks, but this can be uneficient way of solving your issue.