Rather, a toxic asset has the following qualities. It is impaired in some fashion. It is worth less then par. In addition, it is difficult to tell what it is worth. It's value is significantly greater then zero, but covers a wide range of values with a great deal of uncertainty. Like an asset that is worth between 20% and 70% of par.
Also, you need to own enough of them that you can't simply write them to zero or sell them for their lowest possible value or whatever a liquidation would produce.
In order to get a reasonable approximation of ultimate value of a toxic asset, you need to hold it to maturity and just see how much cash it generates.
However, you can't afford to hold it to maturity, since the uncertainty is sufficient to ruin your business.
You can't sell it because there isn't a liquid market for it.
You can't keep it since it is undermining the credibility of your balance sheet.
You can't write it to zero since you would be broke.
If you had enough time, you might be fine, but you don't have enough time.
That is a toxic asset. You can't afford to keep it and you can't afford to sell it. Since keeping it is the "default" you keep it until it kills you. Thats toxic.
The real "crime" of our new toxic assets was their very creation. Once they were created, they became a management problem.