Do you really just rack right into a vessel that you just emptied and left the yeast cake?

No cleaning/sanitizing the vessel or moving the yeast to a different vessel?

Yes, the fementer had beer in it....so if the previous beer wasn't infected, this one will be fine.

What if your using the no chill method? Could the opposite be done by dumping the cake in the beer once it has cooled to pitching temps? I was thinking that on brew day during the mash process I could keg a beer, seal the container with the cake and put it back in the fermentation chamber and use it the next day once the new beer has cooled by pouring it in instead of pitching new yeast. Any thoughts about this? Thanks!

That should work fine. A better method might be;

1. rack finished beer into keg/secondary
2. Wash the yeast cake, or just move it to a sanitized container like a jar or a soda bottle
3. wash/ sanitize fermenter
4. transfer new wort into fermenter, wait for it to cool if using "no chill" method
5. add yeast

Ive done it both ways and both have advantages. FWIW I do NOT do the "no chill" method.

Ok. I should be able to do this then right?. Flame out, cover pot, wait till the next day for pitching temps and then drain wort from pot onto yeast cake. Correct?

The main reason I do BIAB and no chill is for simplicity. Ok, I'm really just lazy but it does work well for me. Now I'm trying to make it even easier by not having to clean the container I racked from the day before is all. Not just to cut costs but time and effort as well.

I wouldn't let wort sit around overnight. You would really risk getting some funky stuff getting in there.

Just did this today racked off the yeast cake prior to starting my brew then left about a cm of the old wort on the yeast than racked the new beer right on top of the cake. Didn't sanitize just pitched. Fermenting like crazy right now!

Seems to be fine, down under it is pretty comon from what I gather. Do some googling.

Is this a technique better done on a yeast cake from a primary or secondary?

Primary