I think nothing will happen. Think about it, you were not born and this planet is 4 billion years old, I would be the same when I am dead, it will be like how I didn't exist in those 4 billion years. But I think that would be soothing in some level, because I suffer a lot in here and I really lack the energy to continue living, and not being existed is no suffering.
But not gonna lie, I feel excited and both worried when I think of nothingness, it won't be all black, I won't be seeing from my eyes, I won't exist at all; when we think of nothingness, we often think that it's all black but it is not, it is not existing in every level, imagine you have no consciousness actually you don't exist at all. I guess it will be like forever sleep without dreaming, but I am glad that I won't exist anymore when I am dead.
I talked too much already but I want to add that we are too used to being conscious because of out nature, so we can't image not existing, we can only relate with it in some way because we sleep, or if you ever passed out sometime, you know, you just don't exist during the time that you are sleeping/unconscious and it is just nothing for you. I hope that happens after death.