If you files a joint tax return for the tax year in question - you both would be responsible for taxes.
If the tax return for that year was not filed - you would be responsible only for your taxes - and not for your ex-spouse.
It is not clear how you filed tax return for 1993... Did you filed as married filing separate or did not file at all?
Only if you filed a joint tax return - you assets might be garnished.
Please provide more details on your situation.