Is it possible to steal proof-of-work answer from a miner who has insecure machine? Consider a miner who has insecure machine found correct answer of proof-of-work and an adversary steals this it and broadcasts to the whole of network to receive the related reward. Is it possible? and if so, what the solution? I do not mean "sealing block" but I mean "stealing nonce" i.e. the answer of pow for a "unique block". Consicer two miners (rational and honest) are working on a the same block. If honest miner can find correct nonce then rational steals this nonce and propagates it in entire network.
The proof-of-work is the fact that the hash of the block is a low number, when you interpret the hash as a long 256-bit number. If you change anything in the block then the hash changes and is very unlikely to be low enough (below the target), so the proof-of-work is gone. And quite right, you did not do any work to create that modified block.
So you can't modify the block after it is mined, which means you cannot change the bitcoin address that this block sends its miner income (new coins and transaction fees) to.
You cannot steal the miner income from a block after the block is mined.
However, if a mining pool server is insecure you could hack into it and make the mining pool mine blocks that pay your bitcoin address instead of their own.
You could also make individual miners in a pool mine for you instead of themselves. They wouldn't even need to have an insecure system. BGP routing attacks have been used to hijack miners before, making them connect to the hacker's server instead of the mining pool server they want to connect to. See https://www.wired.com/2014/08/isp-bitcoin-theft/ This could be mitigated by using TLS, just like web servers use TLS (https addresses).
So there are multiple ways to steal from miners, but doing something with a block that is already mined is not one of them.