In most states, a motor vehicle is registered to the owner of the vehicle. In general, and as a matter of law, the owner of the vehicle is liable for any and all damages that are caused by the vehicle while it is knowingly being used by the owner or by another with the owner's permission.
As long as you own the car (and, thus, it is registered to you), you will be liable for any damages that are caused by that vehicle, whether or not your sister is operating, paying for and/or insuring the vehicle.
The choice is now yours to: (1) give your sister ownership of the car now (in other words, immediately sign the title over to her) and hope that she pays it off; or, (2) keep the title to the car, until you sister pays for it, and hope that she doesn't cause you any legal liability for personal injuries and/or property damage with the vehicle (which is still registered to you) that you put into her custody.
The second choice, which is the choice your question describes has currently been chosen, is much more risky than the first choice. Good luck to you.
PLEASE NOTE: This response is not intended by the Responding Attorney to create, nor does it create, any ongoing duty for the Responding Attorney to respond to this or any other questions. This response does not form an attorney-client relationship with the Responding Attorney, nor is it intended to be anything other than a statement of the educated opinion of the Responding Attorney. This response should not be relied upon as legal advice from the Responding Attorney and is based solely upon the limited facts being provided to the Responding Attorney by the person asking the question. To the extent additional or different facts exist, this response might possibly change. Responding Attorney is licensed to practice law in the State of Ohio and, unless otherwise stated, this response is based solely upon Ohio law.
In most cases, liability follows the owner of the vehicle. Of course, your insurance company, if she were to crash, would look to a subrogation claim against her insurance carrier to pay them back for anything your insurance company pays. It would be wise to not remain on title if you are worried about her crashing--liability could extend to you and your insurance.
This should not be construed as legal advice or the making of an attorney-client relationship. this information is purely for informational purposes and should be treated as such.
Generally speaking Yes, under Michigan's owner liability act you could be liable for your sister's negligence. Also, depending on her driving record, there is a common law theory of negligent entrustment.
Of course, this is not meant as legal advice nor does it establish any professional relationship.