Based on my understanding, blockchains are stored on each node. Each node has a copy of the current blockchain and are updated whenever there is a new valid transaction. But what if all nodes stopped working? For example, there are 1,000 people currently using bitcoin. What if the computers of these 1,000 people stopped working? What will happen to the network? What if there is a new person not included in that original group of 1,000 people tried to run a blockchain client?
Without nodes in a network, there is no network.
In the situation where the 1000 nodes (or even a subset of them) suddenly came back online, the network would simply continue where it left off.
In the situation where all nodes went offline, and all existing data was lost, then the network would begin from scratch with a new blockchain whenever the nodes came back online.
Keep in mind that data loss of the blockchain is highly unlikely. Since there are so many copies, it would take a fairly catastrophic event to destroy all copies. In all seriousness, it's more likely that all members of the human race will be destroyed than it is for all copies of the blockchain to be destroyed. Assuming that a copy exists, the network can always be restarted from one or more backups, and conflicting backups will follow the consensus algorithm to determine which version is more "correct".
Bitcoin is extremely resilient.
If no full node is present, then the network will not exists. Therefore no new client can use that network.