If I left my kitchen (or set of kosher dishes, etc.) with someone who is a) not Jewish or b) Jewish but not shomer Shabbos--in such a way that they could access it and hypothetically do anything they wanted with it--does my kitchen lose its presumptive kosher status? Would this depend at all on my own confidence (or their affirmations, etc.) that the person had not done anything wrong?
Despite the wording of my question title, it is actually hypothetical, and I am interested in both the l'chatchila and b'dieved cases.