I was travling to Israel, and my friend sent a package with me for his sister. We stopped in Europe for 2 weeks, and when we arrived in Israel we could no longer find the package. I have no clue what happened to it: it might have been stolen, lost, or misplaced (I saw it at some point in Europe in my suitcase). Must I pay my friend for the loss, or should I offer to do so?
You are not liable to pay for the loss.
Sources: By accepting to take the package, you became a shomer chinam, an unpaid guardian for the package. Unpaid guardians are liable to pay for losses due to negligence, but not for other losses. The question is how to define the loss of the package. The Gemara (Bava Metzia 35a, 42a) states that a guardian who places the item in a certain place, and does not recall where, is considered negligent. However, Ritva (35a) writes that this is only because the guardian placed the item in a place where he was likely to lose it, which is considered an act of negligence. Therefore, in our case, where you did not do such an act, you would be exempt. Your case would probably be considered a case of aveidah, for which an unpaid guardian is exempt from payment. Furthermore, as you say, it might have been stolen, and the circumstances of its dissapearance are unknown, so that you are not liable to pay for the loss.