Does the IRS investigate USCs and LPRs residing overseas ?

The short answer is yes, with varying degrees of investigation; reviews or audits.  Of course, not all individuals are audited or investigated.  However, the new data that will be collected under FATCA will be an increasingly valuable source of information for the IRS.
In practice, the IRS automatically generates “substitute for returns” for individuals living overseas where no U.S. federal income tax return has been filed.  In these cases, the IRS is receiving some type of income information (e.g., from a bank or broker) and then issuing the substitute for return.

First, there has been a much greater focus during the last 6 years on foreign, international tax matters.  That focus continues under the current Commissioner.
Second, the IRS has been opening offices internationally in different countries.  Most recently, an office in Beijing, China.  
To learn more about the functions of the Tax Attachés (TA) and Deputy Tax Attachés (DTA) and how they serve in the IRS overseas Posts, see the IRM, 4.30.3  Overseas Posts .
Third, with additional information that will be collected under FATCA (starting in 2015 for information for the calendar year 2014), the IRS will have additional information to sort, examine, audit, etc.  This will undoubtedly cause more substitute for returns to be automatically generated by the IRS for those individuals who have not been filing U.S. income tax returns.
Fourth, the offshore voluntary disclosure program has been a treasure trove of information for the government regarding non-U.S. banks and non-U.S. advisers (bankers, accountants and attorneys).
Fifth, the deferred prosecution agreements entered into with various Swiss financial institutions will be an additional source of information regarding USCs and LPRs and their accounts and assets.
Sixth, the IRS has developed a number of methods of collecting, sorting and identifying information (including the information that will be collected above).  For instance, in the Internal Revenue Manual provides the following, regarding USCs and LPRs, including those living overseas -

Section 18. Locating Taxpayers and their Assets (Cont. 1)

* * *

5.1.18.13.3  (05-20-2008)
Using Passport Information

1. Use any new address or new asset information received from the passport office as discussed above.
2. See IRM 5.1.12.25, Outgoing Mutual Collection Assistance Requests, if you determine that the taxpayer:
   1. resides in a treaty country, or
   2. has assets in a treaty country.

5.1.18.14  (03-27-2012)
Treasury Enforcement Communications System

1. The Treasury Enforcement Communications System (TECS) is a database maintained by the Department of Homeland Security (DHS), and it is used extensively by the law enforcement community. It contains information about individuals and businesses suspected of, or involved in, violations of federal law.
2. For IRS field Collection,TECS provides two sources to help make contact with taxpayers or locate assets :
   1. Revenue officers can request that delinquent balance due taxpayers be entered into TECS, and the Department of Homeland Security (DHS) will then advise IRS when those taxpayers travel into the United States for business, employment, or personal reasons. The taxpayers entered into TECS for this purpose are on a DHS lookout indicators list. IRS employees must help maintain the TECS database by requesting that appropriate taxpayers be entered into TECS or be deleted from TECS. (See IRM 5.1.18.14.6.1 for criteria for including taxpayers in TECS data base.)
   2. Revenue officers can also request information housed in TECS on past travel that a taxpayer has made to and from the United States.

5.1.18.14.1  (03-27-2012)
TECS: DHS Lookout Indicators

1. Many of the taxpayers entered intoTECS for a DHS lookout indicator are International ones because the cases usually concern persons who reside abroad. However, domestic taxpayers may also be entered intoTECS if we have been unable to locate them and if they are believed to travel outside the US . Taxpayers placed onTECS are often not subject to ordinary administrative and judicial collection procedures because they frequently reside outside the jurisdiction of the US Courts. Information derived from placing a taxpayer onTECS can facilitate contact with these taxpayers or provide asset information which, in turn, may facilitate collection of their delinquent liabilities.

   Note:

   IRM 9.4.2.4.2.5.3, Other IRS Functions, also discusses TECS and prescribes the use of Form 5523, TECS Query Request, to request information from TECS. However, SB/SE Collection Field (FC) employees should not use Form 5523.
2. Consider the following example as an illustration of how using TECS to place a taxpayer on the DHS lookout indicator list could help in yourcasework.

   Example: A FC RO has a balance due taxpayer in his/her inventory and he determines the taxpayer resides in Norway. The RO transfers the case to International. The International RO determines the taxpayer is “Unable to Contact” and closes the case from open inventory. The RO requests that the taxpayer be placed on TECS. One year later, the taxpayer travels to the US and initially arrives at an airport in New York. Upon the taxpayer’s arrival, Customs and Border Protection (CBP) informs the TECS Coordinator where the taxpayer is ultimately traveling to, how long the taxpayer plans to stay, and on which flight(s) the taxpayer will be departing. The taxpayer will be staying in Denver for one week. The ROs who had previously worked the case had not been aware of any connection the taxpayer had to Denver. The TECS Coordinator notifies the group manager (GM) in International who is responsible for cases in Norway (the country in which the taxpayer resides). The International GM issues an OI to the Collection group working the location in Denver where the taxpayer is staying. The GM in Denver assigns the case to an RO, and the RO meets with the taxpayer and secures a financial statement. When this happens, the IRS learns about the taxpayer’s assets for the first time as other research methods and attempted contacts were unsuccessful. The RO provides the information to International and closes the OI. After the OI is closed, the International RO does further research once he/she is aware of the Denver nexus. He/she discovers the taxpayer has real property held in the name of a trust and files a nominee lien.

   
    http://tax-expatriation.com/2014/07/22/does-the-irs-investigate-united-states-citizens-uscs-and-lawful-permanent-residents-lprs-residing-overseas/