Avoiding IIR instability in DAC

We use 16bit 16ksps CODECs and have some problem when our central DSP inserts a "zero-signal" when squelching an audio input that have no sufficiant audio energy: that squelch is randomly causing our DAC to produce self oscillations in frequencies higher then the 16khz sampling of our system. We think it is the IIR instability for no-signal at the DAC, as the DAC has decimating post filter that may not designed to handle sero-signal conditions. Do anybody knows a work-around for this fenomenom, or a better CODEC DAC that is better behaved in this situation? Is gradual squelch helps? Is a "non-audio" tone injection may help?

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