Can a car be repossessed over having liability coverage insurance instead of full coverage?

If the lender required full coverage (to protect their interests) as a condition of the loan and you drop it and replace it with a liability only policy, then you have breached the terms of the loan. The lender now has the right to declare the loan in default and demand immediate payment in full of principle and interest. Failure to pay as demanded then gives them the right to repossess the car and have it auctioned. If the auction does not get enough money they can sue you for the difference!