Could it be possible that the FTX-Hacker / Drainer stake eth and/or do somehow harm to the network?

Quick thought and question:

Could the FTX-Hacker / Drainer just stake their (flagged) eth and let the rewards send to another adress and generate non flagged eth? Or are the rewards direktly paid to the stake-adress? So even he/she has no option to sell those tokens, he/she could make useable profit from it?

Another question:

Could someone with such a stake (illegally- / criminally acquired) do harm to the eth-network somehow?