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.