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.Open DWG file Open DST file
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