You’re still talking a networked system which needs to be internet-accessible. Servers, bandwidth, storage, and operators are not free and that means someone has to see some value to running them.
The point is that the rewards are elastic. If less people run them, rewards increase, so more people run them again. Obviously the currency rewards are denominated in could hit $0, but that doesn't seem likely to most people at this point.
That's a distraction from the real problem: what value does someone get for keeping a blockchain running? If the founders of the project have walked away from it, how many volunteers are going to care to support an orphaned system at all rather than putting their resources into something they can get paid more for?
The usual answer would be to keep a pet project alive but that runs into the realities of blockchains: the technology is inefficient by design and that means that most of the real work and data happens off chain. Having a copy of the chain itself is likely of minimal value if the company hosting referenced data stops paying those bills, an oracle is no longer available, the client application stops being developed or is not released by its owner, etc.
This means that you can't say anything about the long-term survivability of the chain itself without saying what it's used for because that'll tell you both how many people care about it at all and how committed they'll be to continuing to maintain the chain and its clients.
Do you mean people running the infrastructure? Or developing the software? We don't have to speculate on either. The infrastructure / nodes are paid for by some combination of inflation (block rewards) and transaction fees, depending on the network. The software is pretty similar to any other open source software. There are open source devs who will contribute for free, companies who will give grants for features they have a vested interest in (or will pay their own engineers to develop them directly), and organizations with funding to pay engineers.
Again, we don't have to speculate. We don't even know who the founder of Bitcoin is and it's still under active development.
I'm aware but that wouldn't apply if Google launched a blockchain, which was the origin of this thread, and it wouldn't help with the details I listed where key parts of the system are not stored on the blockchain. If Google introduced, say, oracles which their smart contracts relied on you'd need a way to provide a new service and permission to update those contracts (this is, of course, a massive risk for fraud so that can't be done lightly).
Similarly, even if they used someone else's chain like Ethereum, if the data stored on the chain references something like a CDN endpoint where the real payload is available, the fact that the blockchain itself is still running wouldn't help you much if you didn't have a compatible alternative with a copy of the data.
Major blockchains are by definition the survivors at this point, but a great many have already bit the dust. In the end the single point of failure is always going to be the value of the coin on the open market, 100% of 0$ doesn’t pay server costs.