The spec for method javax.lang.model.util.Elements.getAllMembers() says:
...
Returns all members of a type element, whether inherited or declared directly. For a class the result also includes its constructors and *initializers*, but not local or anonymous classes.
...

But, in fact, getAllMembers() does not return initializers. For example, the following TestProc processor does not print out initializers defined in Source.

--
public class Source {
     static {}
     {}
}
--
import javax.annotation.processing.AbstractProcessor;
import javax.annotation.processing.RoundEnvironment;
import javax.annotation.processing.SupportedAnnotationTypes;
import javax.lang.model.element.TypeElement;
import javax.lang.model.element.Element;
import java.util.Set;

@SupportedAnnotationTypes("*")
public class TestProc extends AbstractProcessor {
     public boolean process(Set<? extends TypeElement> set, RoundEnvironment re) {
         if(re.processingOver()) return true;

         TypeElement te =
                 re.getSpecifiedTypeElements().toArray(new TypeElement[0])[0];
         for(Element e: processingEnv.getElementUtils().getAllMembers(te)) {
             System.out.println("e: " + e + " " + e.getKind());
         }
         return true;
     }
}
--

The result is something like the following (there are no any initializers):
e: getClass() METHOD
e: hashCode() METHOD
e: equals(java.lang.Object) METHOD
e: clone() METHOD
e: toString() METHOD
e: notify() METHOD
e: notifyAll() METHOD
e: wait(long) METHOD
e: wait(long,int) METHOD
e: wait() METHOD
e: finalize() METHOD
e: Source() CONSTRUCTOR

It looks like the implementation does not comply to spec.