Typically, no, junk car buyers will not buy a car with a lien. All liens must be paid off and handled before junking your car.
Junk car buyers can only purchase vehicles from the legal owner of the vehicle, and a lien means the lender or someone else has a legal claim to the vehicle. So if there is a lien that means someone else is the legal owner until the lien is paid off. And the ownership of your vehicle can not be transferred to a junk car buyer until the lien has been released.
If you are looking to sell your junk car with a lien, just pay the lien off first, and then you can sell it.
If you owe more on the car than it is worth, selling the car may not make sense because you will have to pay out of pocket to pay off the lien. And this is typically the case for most "junk" cars. It may make more sense to contact the lien provider and see if you can surrender the vehicle to them or negotiate a settlement that makes sense.
