Let's take example of Bitcoin. Assume all nodes of Bitcoin network go offline for some reason. Now assume an adversary (a party who wants to do harm to Bitcoin) detects the situation and starts mining blocks. Since no one else is mining at that time, the adversary can create selfish (illegal) transactions and include them in his/her blocks. If he is able to build many such blocks on top of each other, when the parties start getting back online, they may have to accept those blocks with selfish transactions (since the longest chain wins). If those blocks are accepted, the adversary has been able to successfully do illegal transactions.