Worrying and fretting is where low self-esteem starts. Just shutting down is where it leads. This is the first hurdle to get over. Children whose self-esteem is so low they will not even try are misunderstood and often dealt with in harsh and destructive ways. Adults may see them as bull-headed, oppositional, and defiant. The child's self-esteem problem looks to them like a behavior problem. From that perspective, they can quickly become frustrated, angry, and down on the child. It is a vicious circle. The child does not try to do things because he believes he will fail anyway. He thinks he will get bad reactions from people no matter how he does. Adults see his behavior as willful and defiant. They get upset and angry with him which is what he thought they were going to do. It makes no difference. Bad reactions and rejection come anyway. From the child's point of view, he is simply someone to whom others react badly; and he does not have to do anything to get the bad reactions. As the saying goes, "Damned if he does and damned if he doesn't;" so why should he bother?
Interpret your child's behavior in literal terms. He does not start projects or try new things, makes no effort to participate, and always has excuses such as "I forgot."
Managing this behavior is difficult; but nonetheless, use this approach. Your first goal is to get your child to start or at least try, not to get him to finish or do well. Any effort he makes is a very big step in the right direction. Trying one problem, at least going to the activity, or making a little effort to do what you expect is progress.
Do not get angry or frustrated with him; for if you do, you would have done better by doing nothing. The same holds for threatening and pleading with him. A better approach is to offer him something he wants if he will just start and at least try. This might be a small privilege, a special treat, time doing something fun with you, or anything else he values.