According to Einstein, energy is the same as mass. Since the sun gives off light, also known as energy, we can assume that it sheds mass, too. It is a lot of mass. It gives off 4 million metric tons of mass per second to be precise. That seems a little excessive and hard to grasp. It is a lot, but not in the grand scheme of the universe and the size of the sun.
The sun weights 2 times 10^33 grams. At its size and the mass it loses, it would only lose about one percent of its mass in about 160 billion years. So, it really isn’t that much when you do the math. Solar wind is a bigger concern than losing mass at a normal rate. Solar winds cause the sun to lose its mass much faster and that is a problem.
The problem is that solar wind is the result of high pressure on the sun’s atmosphere blowing off particles at a high speed. They fly off so fast that they escape the sun’s gravity field and fly off into space.