If a car has been charged off and a collection agency tries to start collection procedures again, would they be able to place a lien against a new vehicle?

A charge off has NO bearing on you. Its simply a tax maneuver on the part of the creditor. Depending on the type of loan used to purchase the car its possible, that they can attach current assets.

Ok, charge off is only a tax term used to save them money for a bad debt, the collection company can still sue you and get a judgement, if your state allows, they can garnish your wages, attach money in your bank account,

So there are many things they will do before they try an get a lien on another car ( but they can in many places)