Infinite fermentation?

[Bolverk]

Howdy all,

I thought of something I'm sure others have as well, but being that I don't know what the proper name for it is, it made searching difficult... I wouldn't call it continuous fermentation as I've seen what that process looks like and this ain't quite it, but the thought is similar.... maybe infinite fermentation?

Say you have 20g fermentor and are fermenting 15g of molasses wash. Your wash/beer is done with primary fermentation and you pull out 10g to run in the still. You put back the 10g worth of fresh molasses wash back into the fermentor to let your yeast get back to work. And when its done you pull off another 10g, and rinse and repeat...

I'm hesitant to call this a dunder pit as it has no actual dunder (backset from the boiler). Is this a "live pit"? The concept of the dunder pit/muck hole, etc is rather confusing as there doesn't really seem to be a standard I can find.

Best I can estimate this would be closer to a sour mash concept, but I don't know if that's a thing for rum. I'm not quite ready to do the whole infected pit thing yet, but was hoping this might get me in the right direction.

Thoughts?
Is this a thing people do?
Is this a dumb idea?
Should i actually add dunder to this?
If so how much?
Is this worth the effort?

Thanks in advance,