Static discharge and earth wire are more for a human safety rather than a component or appliance safety
So what does the earth wire do?
Some devices, example (Televisions, toaster, washing machine, etc) leak current in the body of the equipment. This can happen due to any malfunction or any other reason. Now with no earthing cable, that current stays in the equipment body and as soon as you touch it , it flows thorough your body into the ground (As human body is an excellent conductor of electricity)
If you dont have earthing in your house, Always follow these safety steps
1. Always wear a rubber slippers when touching any electrical stuff that powers directly from the socket and ensure that your feet are not wet (stabilizer, washing machines, lamps, etc)
2. If possible hold a wooden material in your other hand
The purpose of wearing slippers and holding wooden block is to avoid the current passing through your body
And lastly, it always advised to have a earth wire installed in you house. You dont need to a very expert person. Its fairly simple
1. Dig a 7 feet deep, 3ft x 3ft pit in the ground
2. Place a thick copper plate (0.5 inch thick approx with a solid copper wire connected to it) at the bottom of the pit
3. Fill the pit with charcoal and sea salt (you would need approx 2 boris of sea salt and 2 bags of charcoal)
4. Now Fill the pit with water
5. When the water dries up, fill it with sand and close the pit
6. The solid copper wire coming out of the buried copper plate is the earth wire, connect it to the earthing requirements on your house
Now, the technical part is , the depth of the pit is dependent on the soil resistivity and other factors. In developed countries and in big industries in pakistan, the proper way to get a soil test done and then design a proper earthing system.
Here in Pakistan, in home, people just apply a thumb rule (dig a xx feet deep and you are good to go ) and it works well. Same is done in my house.
hope it helps, stay safe and always educate your friends and family on these things.
P.S always keep a fire extinguisher and fire blanket at your home (it costs PKR 5,000 for a 5kg fire extinguisher and 1200 for a fire blanket)