Clamp a D/A to prevent output below 0V
You could use a precision rectifier, something like the below circuit (you can modify the op-amp type as required, note the kink in the time domain where the op-amp recovers from saturation). 







simulate this circuit &ndash; Schematic created using CircuitLab



This will get down to within uV of zero depending on the op-amp. If you need to go a bit lower, bias the top end of R4 with a suitable resistor to a negative source. Eg. a couple M ohms to -5 will allow it to go to -10mV. 

If it's actually going to go below zero in normal operation and trigger the recovery from saturation you could find op-amps that recover faster (very few are actually rated for this operation) and/or you could use a different circuit such as this one: 







simulate this circuit

There will still be a bit of distortion at the zero crossing because the op-amp output has to slew from -0.7V to +0.7V and that can't happen instantly, but there is no saturation.