If the FBI subpoenas a person's credit record, the target of the investigation won't see that on his credit report. Similarly, if a person's emails are being monitored, the target won't see any indication of that.

If the target of an investigation is under physical surveillance, it is possible that the target will detect this. Physical surveillance is expensive and relatively rare.

A person's residence abroad complicates investigations. However, the United States has Mutual Legal Assistance Treaties (MLATs) with numerous countries, and the FBI has legal attaché offices at some U.S. embassies:

https://www.fbi.gov/contact-us/legal-attache-offices

If the target of an investigation is using an American phone service, email provider, or messaging app, the FBI could directly subpoena the service provider. Assistance could also be sought from foreign governments.

In addition, if a target's mobile number is known, technical means exist to monitor that number's calls, texts, and location data exist owing to weaknesses in the SS7 protocol used in cellular telephony:

https://en.wikipedia.org/wiki/Signalling_System_No._7#Protocol_security_vulnerab...

In short, if a person is under criminal investigation by the FBI, that person probably won't know about it until he or she, or an acquaintance, is contacted by the FBI.

Aside from having the FBI knock on your door asking you to answer a few questions, is there a way to tell if you under criminal investigation?  I am not talking about for a security clearance.  I am referring to the FBI suspecting you of a federal crime.

Are there any signs like your credit being checked, ways to spot surveillance, or anything of the sort?  Can a person tell if their emails are being monitored?

What if you live in another country, does that limit how much investigating the FBI can do on you?  Can the FBI monitor any of your phone calls or app messages if you are in another country?  If so, how?

- Person of Interest