bitcoin is a decentralized currency which works based on its users or peers on the network. as long as there is at least 1 peer on this network who has the blockchain, or in other words runs a full node, and as long a he mines bitcoin, it will remain alive.
note that if everyone stops mining bitcoin and that 1 peer is left, the difficulty will also drop down and it won't be as high so it will be easier for him to mine bitcoin.
p.s. bitcoin is just starting, why would it stop at the beginning?!