A case closed without further action is a decision by the judicial system* not to bring criminal proceedings against a suspected offender due to insufficient evidence, lack of expediency, or for reasons of judicial priority or the statute of limitations. This decision, based on an assessment of the facts, is not final and may be revoked if new evidence comes to light, or if the victim takes the initiative to refer the case to an investigating judge or to summon the perpetrator directly to court. Currently, when a victim of sexual violence files a complaint (which is already rare), there is more than a 50% chance that the case will be dismissed.

The main difference between a decision to close a case without further action and a dismissal is that the former is a decision taken by the public prosecutor during the preliminary investigation phase, while the latter is a judicial decision taken by an investigating judge after a judicial investigation.

* In Belgium, the decision is taken by the public prosecutor.

Sources: 
Belgian courts
Amnesty