It triggers upon waking up three days after doing the fourth kennel scene (counting the first one that triggers automatically). The problem right now is that it's become too easy to reach max submissiveness without having enough time to trigger the kennel ending. I'm going to adjust the numbers on that in the next version to make it easier as well as adding a way to check and lower the submissiveness stat but if you want to see the ending in your current save, there should be a way. If you're playing locally (downloaded the game), the easiest way would be to open your save in a text editor and manually lower your submissiveness after the fourth kennel scene or just whenever you feel like you're getting too close. I can provide instructions for doing so if needed. If you don't want to do that or if you're playing online, there may still be a way depending on how far along you are and your luck.
The first time you wake up with a submissiveness over 50, a unique scene is triggered (and I see now that part of it is missing so it doesn't really make a lot of sense). In this scene you are given two options, refusing to work or going back to work. Refusal lowers your submissiveness by 5 so pick that option. Here it gets a bit finicky. If you know at this point how many days are left until the kennel becomes available again (every four days), you have to get your submissiveness back up to at least 50 before that day comes. If you get the fourth kennel scene, you can then refuse work the next day to get sent to the dungeon. Stay in the dungeon for another day, then go back to work. This should trigger the kennel ending upon waking up.
As you can see, there are several problems there. The main issue is that the regular ending comes very quickly after reaching the highest tier of submissiveness (50, the ending triggers at 60) so you have to actively manage your responses to minimize the stat gain. There's also no way to actually see the submissiveness value or to lower it (except for like two or three choices) ingame so if you get too far up the scale it can become impossible to get the ending you want.