Ensure EUIs close themselves (#15860)

Content.Client/NPC/NPCEui.cs

@@ -1,4 +1,5 @@
 using Content.Client.Eui;
+using Content.Shared.Eui;
 
 namespace Content.Client.NPC;
 
@@ -11,6 +12,12 @@ public sealed class NPCEui : BaseEui
         base.Opened();
         _window = new NPCWindow();
         _window.OpenCentered();
+        _window.OnClose += OnClosed;
+    }
+
+    private void OnClosed()
+    {
+        SendMessage(new CloseEuiMessage());
     }
 
     public override void Closed()