Characters aren't specifically given time to pack up and grab things prior to their arrival, however in the case of things like prosthetic limbs, a case could very easily be made to allow the character to either be given it upon arrival or regained early. For the former, it could very easily be hand waved, or the latter route would be an option for an additional 'debt charge'. The Witch would rather have workers around who are at their best capacity to be doing their work, after all! So that is a situation that can easily be worked around.

As for other personal belongings, things that the character doesn't technically have on them at the time they're brought in can still be asked for as a regain, though the 'achievements' section of the regain form is scrutinized a little harder, given the extra legwork involved for bringing belongings in versus simply giving back what was confiscated.