When terrorist states are sued in USA courts, the terrorist states do not pay the fines. There is a fund set up by the US Congress which collects fees from Americans who have done business with states which sponsor terror, as labeled by Congress. Also, funds from terror states are sometimes captured and added to the fund.
At this point there are two lawsuits in progress. Victims and their families of Oct 7 are suing the UN agency for $1B for working to support terrorists; and in the second lawsuit, several billions are sought, if it is proven that Iran, N. Korea, and Syria, all state sponsors of terrorism, are found guilty of supporting Hamas in its training and equipment used against civilians on Oct. 7.
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Source: https://www.timesofisrael.com/october-7-victims-sue-iran-syria-north-korea-for-billions-in-us-court/