Is it illegal for a company to continue to take out money for health insurance that it hasnt been paying?

1) It is not legal: in fact, it is a form of theft--they are taking money of yours that they are not entitled to, since you had only consented to allowing it to be taken out to provide you with insurance, but you are not getting the insurance. You could sue them for the money they took out, which will be complicated, unfortunately, by the bankruptcy.
2) It may be sufficient to terminate the non-compete. Certainly, if the non-compete is part of a larger employment agreement which guaranteed you health insurance, then their breach of a material, or important, part of the agreement would be sufficient to terminate the agreement as a whole, letting you out of the non-compete clause.
If the non-compete is a stand alone agreement, then whether it does or does not terminate it depends on whether a judge (if this were to go to litigation; e.g. they were to try to sue you for violating it) would conclude that continuing to charge you for health insurance without providing it was so antithetical to the employer-employee relationship and so unreasonable that it constituted effectively or "constructively" terminating you; if it did, then it would terminate the non-compete. We cannot say definitively whether a judge would or would not feel this were the case; all we can say is that a judge might or could. Unfortunately, there is a subjective element to this (it's in large part up to a judge's personal judgement or evaluation of the situation) and we cannot predict that in advance.