Example 1: I just had an object turn into a cube while I was attempting to slice it into pieces via 3D Subdivision

Example 2: I start subdividing the object and it vanishes. I have done a lot of subdivision on the objects in this file and this is the only one that vanishes.

Before:

After:

When this happens, undo the subdivision, then modify the default subdivision options in Options>3D View>3D Subdivision:

Toolkit - try switching the setting to the opposite of whatever you have now.

The reason this setting exists is to cope with different CAD software. For example, surfaces from AutoCAD Civil 3D models almost always disappears when using 'Advanced' toolkit (switch to 'Simple' would normally help).

Triangulation type - try switching to Always Triangulate
Try sewing to solid - try turning this option on or off

You might have to try different combinations of the above. Please note that changing these settings only affects future subdivisions and not ones that are already made.
If you want to change the settings for an existing subdivision, you will have to change the settings and then edit that subdivision (by moving the slider or increasing then decreasing the number of subdivisions for example).