All UK citizens and their (non-EU) family members who were lawfully residing in the Netherlands and the other EU27-member states at the date of the UK’s withdrawal can stay after Brexit. They have to meet the same conditions that existed before Brexit.
This also means that the right of permanent residence after 5 years living and working in the Netherlands, will be retained after Brexit. With permanent EU residence, one is no longer subject to any conditions, such as to continue being a family member and or to continue working. Also the right of permanent residence as a result of permanent incapacity to work caused by an accident at work, will be retained.