The problem here is what do you mean by "show experimentally by taking an example."
-If you meant astronomical examples of this happening to other sun-like stars in space, you would have to search things like "red giants" and "planetary nebulas" and the like for more information.
-If you wanted to know if you can perform experiments that mimic the death of the sun, then no, we have not achieved sustained, controlled thermonuclear fusion which is what powers our sun. Since we cannot create the process that creates the stars, we cannot "experimentally" mimic the death of the sun this way.
-If you wanted to show by mimicking what most scientist believe will happen to the sun based on observations from similar stars in space (which I guess is what you are going for since I am pretty sure that you do not have access to fusion reactors) then my suggestion would be to get a fish tank (or something similar), a balloon, an air pump, some glitter and some clay and some sticks.
Add some glitter to the balloon and have it attached to the air pump in the center of the tank. Use the clay to make round "planets" at the end of the sticks. Place "Mercury" really close to the balloon (your sun), then Venus , then Earth etc. Then turn on your air pump and watch the balloon (sun) "gobble up" the planets one-by-one. Finally let your balloon (sun) burst (by pricking it) inside the tank spreading glitter (stardust) in your space (fish tank).
What this demo does is illustrate the red giant and planetary nebula phase of the sun.
For more information on the physics of the suns death you can check out this site http://www.enchantedlearning.com/subjects/astronomy/sun/sundeath.shtml
The information is presented in an easy language so you should have no trouble following along.
Also if you do decide to do the demo in your project make sure that the balloon is big enough to gobble all the inner planets. You can also personalize it by having a red balloon (red giant sun) and different colored planets (Mars=Red, Earth = Green/Blue) for "coolness" points.
Enjoy and let me know if you have any questions.