We teach (ad infinitum....) that a more reactive halogen will displace a lesser halogen from a compound. And yes, the halogen is a halide ion in the compound. Now I think about it, it's usually in solutions, so the halide is nominally solvated and surrounded by water (as hydronium ions?).
Does the halide lose the electron to give a radical, or does the halogen dissociate to radicals, or to ions, or is there an intermediate Cl2- ion, for example? I realise this is several questions, but the major question is unaffected by my speculation. All I have found is the bald statement about displacement and reactivity and the table we always draw.