It can certainly find bugs, but it is not proof that all is well.
Getting all green lights on a test suite does not necessarily mean that everything is okay. It is quite possible for bugs to still exist in a system, even when the code coverage is quite extensive.
Still, it is worth trying to cover all the known cases. More coverage and test cases is better than less.
You just have to remain vigilant. Don’t put all your faith in the testing machine.