The implication here is that maybe the cofounder's 'next business' is the same business with a different back-end and that the market presence and customer base (which absolutely are assets of the current business) are being carried forward. If this is the case then the OP has a valid claim to any profits generated by those assets, or to being bought out.
The business's legal entity is being shut down and closed. The OP only has claim over assets of that business. If he agrees to certain assets being given to the other partners, he has no claim for the future use of those assets.
Of course, if that's part of the split (you take the code you wrote, I take the customers I sold to) then there's no future claim. The way I read it, there was no discussion of that, but maybe I'm wrong - after all we don't have much to go on here.
