Firstly -yes, it is quite commonly used. The literal meaning of 'tumbling' is falling and bouncing. So - a pile of rocks would tumble down a hill if pushed over. If you knock over a construction of children's bricks, they are also said to tumble. Another similar use is for acrobats and gymnasts - the moves they make when rolling around the floor is also called tumbling. To describe a statue as 'tumbling' is a little of an exaggeration, as they typically don't bounce much! This is typical of journalists, who like to use quite varied language. 'The world is tumbling down' is obviously very figurative, and something of a stock phrase - but it does describe the way that things often fall apart, with the structures of society breaking up, and 'rolling around', and sometimes breaking other things, before finally settling down in a new form.

I mostly see the phrase "tumbling down" used in relation to something that ended quickly, that when it came down, it created a ripple or domino effect, or that many things are ending or in a bad state at once. For example, your phrase "the world around you is tumbling down" would mean something like many things are going wrong in your life at the same time. Maybe you lost your job, got divorced, and the dog died.

the big things or some systems are collapsing down,which means all is over without possibility of rerect or rebuild. something devastated in a whole