Connecting a battery powered circuit to the earh ground
In the absence of a ground, how you choose to label the nodes in the circuit is entirely arbitrary.  You could use +4V and 0V (which is more conventional), or +2V and -2V, or 0V and -4V.  Because you can only measure voltages between two points, it's up to you to choose which point you consider to be 0V and measure relative to that.

By convention, the Earth is at 0V.  So if you tie one line to ground, that will now be at 0V.  Doing so has no effect on the circuit - you've just chosen which line is now considered to be 0V.

There are no real-life applications of this.