That actually isn't true any more. There is a salary floor where each team has a minimum they have to spend. I couldn't tell you exactly how much it is but I know it's pretty high.
According to the CBA's Article 12, Section 9:
A) For each of the following four-League Year periods, 201 3-201 6 and 2017-2020, there shall be a guaranteed Minimum Team Cash Spending of 89% of theSalary Caps for such periods (e.g., if the Salary Caps for the 2013-1 6 and 2017-2020 are$100, 120, 1 30, and 1 50 million, respectively, each Club shall have a Minimum Team Cash Spending for that period of $445 million (89% of $500 million)).
If a team fails to meet that standard, the CBA continues:
B) Any shortfall in the Minimum Team Cash Spending at the end of a League Year in which it is applicable (i.e., the 2016 and 2020 League Years) shall be paid,on or before the next September 15, by the Team having such shortfall, directly to the players who were on such a Team's roster at any time during the applicable seasons, pursuant to the reasonable allocation instructions of the NFLPA.
http://www.thephinsider.com/2013/2/17/3997314/nfl-salary-cap-2013-amount-salary-floor