NO. If the lender is trying to repo the vehicle and they can't find it,they cannot report it as stolen. Only the owner can do this. "STOLEN" is defined as "unlawful taking". You did not "take" the vehicle unlawfully. If you refuse to surrender the vehicle the lender may get a judgment (Writ of Replevin) and have the Sheriff's office come knocking on your door and only then will you have to surrender the vehicle or tell them where it can be located. Why stress over a vehicle? The value keeps going down and there are plenty of cars out there to buy. If for some reason, such as illness, loss of job, etc., where you cannot make the payments and no hope of making up the late payments, call the lender and have them pick up the vehicle. You'll get another vehicle one day. Just remember to remove your belongings and the plates. If you added anything on the vehicle you can remove that to. The lender doesn't know if you put in a new stereo system, and the car and everything in it is yours until it is returned.
The thing you need to keep in mind is that the lienholder IS the owner of the vehicle. Until you've paid off that lien, and hold the title in your hand, you do not own that car. Can they report it stolen? Yes, they can. Once you've refused to surrender the vehicle, your retention of it violates the terms of the contract whereby the lienholder (the actual owner of the vehicle) allows you to retain and use that vehicle. So yes, it is unlawful taking at that point. Will it happen? EXTREMELY unlikely. The lienholder doesn't want the car, nor would seeing you go to jail benefit them in any way. For one, it would be a serious PR black mark, not to mention that, if you went to jail, you would lose any employment you have, so how would you pay them back?They'll start by sending notices to give you a chance to respond, and they'll often be willing to work out something with you - again, their interest is in getting their money, not throwing you in jail. If that fails, then the repossessors come. Now, I have heard of recovery agents reporting vehicles as stolen (acting as agents on behalf of the lienholder - the legal owner of the vehicle), after they'd been told, "well, I just don't know where it is", but I've never known any who have actually done this, although I have known some to have filed missing property reports.
If the repossession succeeds, the vehicle will be auctioned off, and you'll be expected to pay the remaining balance owed. Which, you can either work out a payment plan or be sent to collections. If it fails, then they'll typically turn to a civil court, and a judge will order you to pay up or surrender the vehicle. Once that happens, then noncompliance will throw you in jail. A finance company would not, although it is possible.