If you use off-chain data in a stream, then what you say is correct – if nobody in the network has the off-chain data, then it will not be available to the subscriber.
But there is also the option of using on-chain data in a stream, which prevents this problem – the full data is stored inside the blockchain which every node has a copy of. A node does not need to subscribe to the stream to receive on-chain data, and they can choose to subscribe at any time later on.