ayu,
Do you have pictures of the electrodes?
I do not know what you have, but maybe I can give you some things to think about.
silver chloride if heated can decompose to silver and chlorine, But the silver chlorides can also be volatile so you can burn off your silver in the white smoke, so normally we do not want to try and melt silver chloride, we normally change it back to silver metal before melting using one of the conversion methods, like NaOH and karo syrup, HCl and aluminum or dilute H2SO4 and iron, another way is to convert it (or reduce it) to silver in the melt using sodium carbonate in the flux.
Silver will dissolve in dilute nitric acid, silver chloride will not dissolve in nitric acid.
Silver nitrate can be precipitated with HCl to form insoluble silver chloride (leaving nitric acid as the byproduct, if excess HCl used it would form a type of aqua regia, leaving some chloride in solution).
NaCl will also precipitate silver from a silver nitrate solution, leaving sodium nitrate as the byproduct.
Both of the above methods produce silver chloride which needs conversion back to metal before melting as described above.
Copper will cement silver from a silver nitrate solution, or replace the silver in solution, this gives us a powdered silver metal that can be washed and melted without much trouble or loss (the byproduct would be copper nitrate solution).
Silver chloride can be dissolved in a thiosulfate solution, it can be cemented out of solution with steel wool, or electrolysis used to recover silver.
Silver chloride will also dissolve in an ammonia solution, if doing this you should acidify the solution to precipitate the silver from solution and make it safer, as the silver ammonium complex can be dangerous if dried.
Silver metal will not dissolve in thiosulfate or ammonia.
It sounds like you have the silver/ silver chloride separated from the plastic, but at this point you still have a good portion of your silver as a chloride, melting it at this point you could burn off a good portion of your silver as white smoke, to prevent loss of your silver you should to convert the silver chloride to silver metal before the melt, or use a flux with sodium carbonate Na2CO3 also called soda ash, or washing soda, in the flux melt to convert the silver chloride to silver during the melting process.
Edit to add thoughts.
Silver chloride AgCl does not dissolve in HCl (although with high concentration and heat you may put a tiny bit into solution as AgCl2, dilution will precipitate it out of solution, my thought here is that with using HCl to remove the Ag/AgCl form the plastic you could still have chucks of silver chloride (which could be a bit more difficult to convert to silver metal by the normal conversion methods that we normally use on powders, where exposure to each grain of the salt is needed).
