If you're referring to the bitcoin blockchain, yes, it's possible for it to be stopped if a global crackdown on miners takes place and seize all the mining equipment, further preventing the addition of new blocks on the chain. Given the 'decentralized' nature of bitcoin, and its miners being situated into different parts of the world, it would be hard to search all of these and seize it all, so that one possibility is ruled out. Another event that could possibly stop bitcoin's blockchain is a nuclear warfare wherein a huge percentage of the world is completely disintegrated and the remaining are left dying in nuclear waste. We are very far from that happening but it still is a possibility you cannot rule out to happen in the distant future, otherwise the process of adding blocks in the chain is ad infinitum.
Even if all asics disappeared tomorrow, people could simply go back to cpu/gpu mining. Granted, that diff adjust would be painful, but the network would survive.
My actual question is: What happens after the last bitcoin gets mined?. Sure the year 2140 is so far away we may not even see it, but, I'd like to know regardless.