How could chlorine dioxide be stabilized in aqueous solution? There is a water-based mouthwash product which is advertised as having the ingredient "stabilized chlorine dioxide." The only other listed ingredients are trisodium phosphate and citric acid. I assume this is a buffering solution or something. 

In the company's documentation, it says it contains 


  a stabilized molecular form of chlorine dioxide.


But in another location, the company claims that


  the solution is naturally activated by the amino acids in saliva,
  creating a small and very safe amount of chlorine dioxide.


So that sounds to me like there's actually something else in the solution, and the that the $\ce{ClO_2}$ is being produced ("activated") during use. 

I've done some reading, and I have learned that $\ce{ClO_2}$ can be produced in several ways, but all of these methods seem to involve unpleasant reagents like chlorine gas, HCl, or oxalic acid. 

I'd like to know what actual compound might be referred to as "stabilized chlorine dioxide" and what reactions might be involved. 

I'm not asking about the effectiveness of the product, or what value $\ce{ClO_2}$ might have as a disinfectant, I'm just curious as to whether the claims made about the ingredients are plausible, and if so, what reactions might account for this?
Your assumption is correct. The term “stabilized chlorine dioxide” is misleading since the solution does not contain relevant amounts of chlorine dioxide $\ce{ClO2}$.

The solution actually contains sodium chlorite $\ce{NaClO2}$, which is the salt of the unstable chlorous acid $\ce{HClO2}$. At low pH, chlorite solutions contain chlorous acid 
$$\ce{ClO2- + H+ &lt;=&gt; HClO2}$$
which decomposes to form chlorine dioxide approximately according to
$$\ce{5HClO2 -&gt; 4ClO2 + HCl + 2H2O}$$
or
$$\ce{4HClO2 -&gt; 2ClO2 + HClO3 + HCl + H2O}$$

At higher pH, decomposition of sodium chlorite slows down. Therefore, sodium chlorite is mainly stabilized by using a buffered solution. In your product, the buffer consists of trisodium phosphate and citric acid. Thus, a better description would be “stabilized sodium chlorite” instead of “stabilized chlorine dioxide”.