Question: Suppose I want to reduce risk of a circuit breaker malfunctioning and failing to disconnect a shorted circuit.

What if I install two identical breakers sequentially (one after another) so that if one of them fails the other one steps in and disconnects the circuit? Is there any problem with such installation?

Answer: 
There is no problem here.

In fact, this is often how subpanels are configured; the main panel has a breaker that feeds the subpanel, and the subpanel has individual circuits protected with their own breakers. The subpanel will have an amp rating. The minimum of the subpanel rating and the ampacity rating of the wire feeding the subpanel will dictate the appropriate breaker for the main panel.

Appliances that require their own local disconnects (such as air conditioners, water heaters, etc.) frequently use a small enclosure with space for just one circuit breaker. This could be a good option for whatever application you are thinking of.
"Suppose I want to reduce risk of a circuit breaker malfunctioning and failing to disconnect a shorted circuit."

If you have a good quality panel... Square D, Eaton, Siemens, etc.. you really have no reason to worry about a circuit breaker malfunctioning in such a way that it doesn't trip if your load is greater than its ampacity. I have never seen this happen to any manufacturers circuit breakers not named Zinsco. In short, circuit breakers work and they work well you dont have to be afraid of them failing. If you are really nervous, install a arc fault circuit interrupter breaker in the existing ones place... any arcing and it will trip. Or an arc fault/ GFI combo breaker that will protect you from every angle.