The failure of the two lenders is expected to cost the deposit insurance fund $645.3 million combined.
First National, which operated 51 branches, had about $3.1 billion in assets and $2.3 billion in deposits as of June 30.
PlainsCapital Bank, based in Dallas, agreed to assume all the deposits and buy about $2.7 billion of First National's assets.
It also entered into a loss-share agreement with the FDIC on $1.8 billion of the failed bank's assets.
The Community's Bank had about $26.3 million in assets and $25.7 million in deposits as of June 30.
The FDIC was unable to find another financial institution to take over banking operations for The Community's Bank. As a result, the FDIC says it will mail checks directly to depositors for the amount in their accounts that's insured.
The FDIC insures deposits up to $250,000 per depositor.
U.S. bank failures have been declining since they peaked in 2010 in the wake of the financial crisis and the Great Recession.
In 2007, only three banks went under. That number jumped to 25 in 2008, after the financial meltdown, and ballooned to 140 in 2009.
In 2010, regulators seized 157 banks, the most in any year since the savings and loan crisis two decades ago. The FDIC has said 2010 likely was the high-water mark for bank failures from the recession. They declined to a total of 92 in 2011.
Last year, bank failures slowed to 51 — still more than normal. In a strong economy, an average of four or five banks close annually.
The sharply reduced pace of bank closings shows sustained improvement.
From 2008 through 2011, bank failures cost the deposit insurance fund an estimated $88 billion, and the fund fell into the red in 2009. With failures slowing, the fund's balance turned positive in the second quarter of 2011.
The fund had a $35.7 billion balance as of March 31, up from $32.9 billion at the end of December.
The FDIC expects bank failures from 2012 through 2016 will cost the fund $10 billion.