Abandoned billboards bring with them some degree of mystery and risk, so each one is a custom case at best. You may never find the original owner of an abandoned billboard, so your typical starting point is with the land owner. You get the full story of how the sign came to be there and came to be abandoned. In many cases, the current status is that the sign belongs to the property owner as "abandoned property" as well as in trade for years of unpaid rent. But you will never know 100% for sure unless there is a bill of sale from the sign owner to the property owner, or in those rare cases that you ca find the original owner and buy his rights. The permits are just as sketchy. In some areas, the simple existence of the sign creates the legal right to be there, and in others you may be in violation of city and/or state statutes.
Since you never really know if the sign is 100% legitimate, you normally have to roll the dice to some degree. Although I've bought signs from original owners, as well as property owners, most abandoned signs require some leap of faith and risking some cash. I would not take over any abandoned sign that requires much more than putting a new vinyl on it, coupled with some light repair. Making structural alterations without a permit is illegal in most places, and might result in it collapsing. Before you do anything with an abandoned billboard, make sure that it's solid and in good working order (you can hire a sign company to do this for you). If it turns out you made a mistake, you normally just take down the vinyl and you're fine -- which means your risk is basically the cost of vinyl printing and installation.
In my entire career, I only ever had to remove one abandoned sign that had been brought back to life.