Egoistic miners combined with large transactions destroy PoW? EDIT
There is a clearer description of some parts of the problem in the link questions.



If there is a transaction value much higher than the payment for mining 10 new blocks, how can you trust this transaction?

To go more in detail. If I am a bad boy and pay with a proof-of-work cryptocurrency a large sum. Large means that the value is much higher than the payment for mining 10 new blocks. After that I wait some time - for example, so long, that 10 new blocks are mined in between - so that everybody thinks the transaction is sure. Than I bribe the miners with half the value of my transaction to create a new chain without my transaction. Because half the value of my transaction is very much and the miners are egoistic, they will create the new chain to get more payment in this way.

Is there any solution for such attacks in the construction of any cryptocurrency working with proof-of-work?

The only solution I see is, that we trust only transactions values which are comparable with mining-costs. But then the cryptocurrency is very inefficient.
I think what you're describing is a 51% attack, but with a 3rd party that is not a miner, incentivizing the miner's 'bad behaviour'. Even with an off-blockchain bribe, you would need 51%+ of miners to make this attack work (otherwise the 'original chain' would always outrun the 'bribed chain'). 

So, if an 'egoistic' miner wanted to perform this attack, I think it would make more sense for them to do it for their own transaction, not for someone else. Performing this attack with the involvement of a third party only increases the risk for the miner (what if the third party doesn't pay the bribe? etc). I think it makes more sense for a miner to just perform the attack themselves: send 1000 btc to an exchange, convert to altcoin, withdraw, and then roll back the btc chain to remove the transaction that sent coins to the exchange. 

There is a reason this sort of attack hasn't occurred: miners see it as being less profitable in the long run.