What are the chances? Substantially slim that the government can do anything, then the process to go about it would be something else, because you will have to prove that the funds were in truth, stolen. I can imagine losing $300 worth of bitcoin and going to my local police station to make a complain, i doubt if i will be taken too seriously.
There are some chances , but first you have to show the police and mostly the cyper crime special teams enough evidences for what you complaining.
In case of the Fake Malware downloads for Phonixminer we got there is already enough evidence in a few cases and a investigation is started.
It needs the Hacker address where the coins was sended (if a hack was happend) , the malware you have got and downloaded .
Connections to somebody that have access to the chainalysis software helps a lot for find services and exchanges.
But for low Amounts of BTC the expenditure mostly is it not worth to investigate.