“its owner must accept it.” A major theme in the Torah, God’s “instruction book,” is personal responsibility. The point of Exodus 22:10-11 is that everyone is responsible for their own possessions. If a person is unable to watch over his possessions for a time, then he (or she) must be very careful in picking someone to watch his stuff, because if it somehow disappears, the one who said he would watch over the stuff only has to swear he did not take it himself, and the matter is settled. The stuff is gone somehow, but there is no retribution required. The lesson in this is that each person is responsible for his own things. If you must leave something with someone, you have to pick someone that you trust and that you think is also responsible and diligent to keep it safe, and even then if it somehow gets lost you lose what you own. No one is ultimately responsible for your things but you.
But there is an exception that involves risk for the one who agreed to keep watch over the things. If anything is stolen, the one who agreed to watch the things must pay back for what was stolen. He does not have to pay the owner double, but he has to make good the loss (Exod. 22:12). Part of the lesson here is that you do not want to agree to watch over someone else’s things unless you have clear boundaries (“How long will I have to watch this?”) and are quite sure you can indeed keep the goods safe.