[Parameter]
public EventCallback<bool> DropDownVisibleChanged { get; set; }

<DxDropDownBox @bind-Value="Value" QueryDisplayText="QueryText"
            DropDownVisible="@DropDownVisible"
            DropDownVisibleChanged="@((value) => OnDropDownVisibleChanges(value))">
    @* ... *@
</DxDropDownBox>

@code {
  object Value { get; set; }
  bool DropDownVisible = true;

  void OnDropDownVisibleChanges(bool value) {
    DropDownVisible = value; 
    // ...
  }
}