This script would be attached to the same object as our RuntimeDungeon component.

DoSomethingOnDungeonComplete.cs

using UnityEngine;
using DunGen;

[RequireComponent(typeof(RuntimeDungeon))]
public class DoSomethingOnDungeonComplete : MonoBehaviour
{
	private RuntimeDungeon runtimeDungeon;


	private void Awake()
	{
		runtimeDungeon = GetComponent<RuntimeDungeon>();
		runtimeDungeon.Generator.OnGenerationStatusChanged += OnDungeonGenerationStatusChanged;
	}

	private void OnDestroy()
	{
		runtimeDungeon.Generator.OnGenerationStatusChanged -= OnDungeonGenerationStatusChanged;
	}

	private void OnDungeonGenerationStatusChanged(DungeonGenerator generator, GenerationStatus status)
	{
		if (status == GenerationStatus.Complete)
		{
			// Do something
		}
	}
}