As others have said, do not help this person. Three DUIs in many states is a habitual offender. If they were in an accident, regardless of injuries or not, and this person was drunk again, you could even be charged criminally for your role in providing the person with a vehicle while fully aware of the person’s history of drunk driving and being unlicensed as a result.
So yes, you could be sued. You could wind up losing everything sans somewhere in the area of about $4k of personal property. Additionally, your auto insurance will drop you. Not may drop you, WILL drop you and it will hard to find any affordable insurance.
Your money would be better spent on rehab. Although it only works if the alcoholic wants help to quit and based on the fact s/he is wanting you to purchase a car for them to use, I don’t think that’s their case. Save your money for something worthy.