There seem to exist several different dwg to dst conversions, but all of them should be possible. The most typical one is a workflow in AutoCAD, generating sheet sets (.dst) from drawings (.dwg) but that's not really a conversion.
The more common variant of dwg to dst conversion, would be attempt to convert a vector design saved in DWG format to Tajima embroidery design, something you can do in latest CorelDraw.