Can you get title to property through adverse possession for an 1' encroachment?

As long as you have satisfied your state's prerequisites to adverse possession with regard to the 1' piece of land, you may begin adverse possession proceedings. However, since the piece of land is only 1', you should seriously consider not pursuing an adverse possession claim. Not only will you have to pay an attorney to represent you in court, you also have to live next to the neighbor whose property you are adversely possessing. If you want to pursue adverse possession, it is highly recommended that you try mediation before going to court. (See below link.)