There is a dispute amongst the poskim about the status of a utensil that was pickled with a forbidden food. The Shach (יו”ד צח ס”ק יג) writes that the utensils can absorb the taste of the forbidden food through pickling. The Taz (יו”ד קה ס”ק א) rules that utensils absorb very minimally from pickling, and if one cooked permitted food in a pot that absorbed the taste of a forbidden food through pickling, the food is definitely permitted.
If one left permitted food in a pot that was forbidden (through cooking, not forbidden through pickling) for twenty-four hours, both the Shach and Taz agree that the food is permitted to eat. The reason is that by the time the pickling finished, all taste absorbed in the pot from a forbidden food would be older than twenty-four hours, and would not be capable of imparting a strong flavor to the permitted food in the pot. The Mishna Berura (מ”ב תמז ס”ק עא) points out that if a permitted liquid was sharp and it is soaked in a pot which has previously absorbed the taste of a forbidden food, the food becomes forbidden even though the beliyot are not ben yomo. The reason is because sharp can make non ben yomo beliyot into ben yomo.