Government institutions including FBI will not check your wallet for no reason. They will probably have to have some suspicion that you are performing illegal activities or laundering money.
But in general today is very hard to keep your data anonimous because exchangers and wallet have obligation to report the data to governments if they ask if they want to keep their business legitimate.
You know what the government also considers to be a heavy crime? It's tax evasion.
While you are just hodling coins without thinking about declaring your coins to the IRS, you are without realizing it yourself evading tax.
If they spot some sort of suspicious activity with you and your bank account, then it will ring some alarms where they eventually will force whatever service to hand over user information.
It's a nasty method, but is a more than realistic scenario as we have seen with Coinbase. They don't have much to say. They must hand over all the information the IRS is asking for.
