How can I sense if a cane is being held upright or fallen down?
I agree with one of the above replies in that you need something (probably two accelerometers) to detect the angle at which the cane stands (calibrated at the factory if you are industrializing this). This way you have a continuum of what angle the cane is at, relative to upright. 

This gives a distinct advantage over a simple tilt switch for the following reasons. 
1. You can calculate the angle with two accelerometers. With a tilt (on/off) switch, you cannot
2. Not only can you calculate the angle with two accelerometers, you can detect the rate at which the angle changes relative to the cane standing up straight. This is key as you can then at least have the information to characterize what the rate of fall looks like by a simple drop test and base your fall detection algorithm model on that.