And the old chain would be running like it's running now and people would see as much value in it as now because nothing would change. Dogecoin original chain wouldn't have any development, just like it currenty doesn't. It wouldn't make any sense to keep it but it doesn't make any sense at the moment either.
So there would just be 2 chains, some would cash out the other one, the one that they wouldn't agree with.
Fingers crossed there will be two separate chains, as the community disagrees on the PoS model. I don't mind about having a Dogecoin Classic, as long as decentralization wins in the long run. This split could be a great opportunity for Dogecoin holders if it comes into fruition within the not-so-distant future. It'll be "free money" just like the days of the Bitcoin Cash and Ethereum Classic forks. As much as I admire Vitalik's contributions to the crypto/Blockchain space, I think he should focus on ETH instead. Getting involved in Dogecoin will only make matters worse.
Ultimately, the power is in the hands of the community. We'll have to see how everything will turn out to be in the future as Dogecoin becomes more popular in the mainstream world. Just my opinion