If your bank goes bankrupt or runs into trouble, you will not lose all your money. This is because there is a guarantee system in place to help account holders: the Deposit Guarantee Scheme .
All banks holding a banking authorisation granted by De Nederlandsche Bank (DNB) are covered by the Deposit Guarantee Scheme. Your money is safe with a maximum of €100,000 per person and per bank. In general this only applies to your current account and your savings account. Investments are usually not covered. Please contact your bank for more information which accounts are covered.
If your bank has its main office in another country, the rules of that country apply when it comes to a Deposit Guarantee Scheme. It is important to check if your bank has a Dutch licence or a licence from another country. You can find an overview of all banks covered by the Dutch Deposit Guarantee Scheme on https://www.dnb.nl/en/supervision/public-register/WFTDG/index.jsp