Can component invoke a self destroy event

Not sure about the cleanliness of such a solution, but I used:

this.viewContainerRef
    .element
    .nativeElement
    .parentElement
    .removeChild(this.viewContainerRef.element.nativeElement);

Here is another way to do it. This works from within the component itself; no need to communicate with external components.

// imports
export class SelfDestroyableComponent implements OnInit {
    // other code

    constructor(private host: ElementRef<HTMLElement>) {}

    // whatEver function name you want to give 
    onCloseClicked() {
        this.host.nativeElement.remove();
    }

    // other code
}

If you add a component using ViewContainerRef.createComponent() like shown in Angular 2 dynamic tabs with user-click chosen components, then the component can destroy itself when you pass cmpRef to the created component.

Otherwise I don't think there is a way. You can pass a value to the parent so that an *ngIf removes the component.

<child *ngIf="showChild" (close)="showChild = false"></child>

class ParentComponent {
  showChild:boolean = true;
}

class ChildComponent {
  @Output() close = new EventEmitter();

  onClose() {
    this.close.emit(null);
  }
}