Propane tanks do not explode. They do not implode and nor do they rupture or come apart on their own. In fact, bringing a propane tank to the point of "explosion" is a tremendously difficult and time consuming task that's not as simple as most people think.

Is it bad to let propane tank empty?

If you leave a valve or gas line open when the propane supply runs out, it can cause a leak when the system is recharged. Air and moisture that accumulates in an empty tank can cause rust build-up; rust reduces the rotten egg smell of propane, making a leak more difficult to detect.

How likely is a propane tank to explode?

It should come as no surprise that the media is fond of reporting “propane-LPG tank explosions”, even if it did not actually occur. The reality is that propane gas cylinders or propane tanks hardly ever explode.