The “nothing-at-stake” problem refers to the fact that block creators on generic proof-of-stake protocols do not have anything at stake when the network forks. This is one of the primary criticisms of proof-of-stake consensus mechanisms. When a proof-of-work based network, like Bitcoin, forks, every active miner creating blocks on the network must *choose* which fork to mine on. A mining unit cannot create blocks on both forks at the same. The scarcity of the hash power is what forces (in theory) the fork to resolve. When a proof-of-stake protocol forks though, the scarce resource for block production is not hash power but token stake, and, in a fork, an equivalent amount of stake is created on the new network. This means a block creator can start creating blocks on both networks immediately and they do not have to choose (the computation cost of creating a block in a POS system is generally trivial because miners are not competing with each other based on computation). This makes it difficult, if not impossible, for a simple POS system to resolve forks; moreover, it can make double-spend attacks much cheaper in the case of fork resolution.
The industry has been aware of this issue for many years, ever since the first versions of proof-of-stake protocols were released in 2012 and 2013. Vitalik Buterin offered an excellent explanation in a 2014 seminal blog cost covering the topic and Ethereum’s early Casper explanations outlined methods of defense. The original Cosmos whitepaper also discussed several defenses. Most solutions center on punishing block creators if it can be proven that they are creating blocks on another network.