If you or your loved ones are starving, are you allowed to steal food from those who have more than they need? On the face of it, yes, of course: Pikuach nefesh says you can break any commandment to save a life, except those against idolatry, sexual immorality and murder. Stealing is not on that list. Yet I asked that question to more than one rabbi over the years and they always managed to squirm out of it without giving me a firm answer.
The Gemara )BABA KAMA 116B (noted above) discusses saving ones OWN life with someone else's property. [מציל עצמו בממון חבירו] Indeed if one saves his own life, he must pay for the damages. But when saving another person's life one does not have to pay, since chazal were concerned that one may refrain from saving another persons life if he was made to pay for damages done in the process. Which is obviously not a concern when saving one's own life.
Besides for Kesubos 19a (Double AA's comment), which seems to be a daas yachid and rejected, a principal source is Bava Kama 60b.
The Gemara discusses "saving one's life with another's property" (in the context of damaging it during a battle- though I don't see why stealing would be that different), and seems to conclude that it is forbidden- although a king would be able to.
However Tosafos and the Rosh insist that since it's not one of the 3 aveiros it must be completely permitted. They interpret the Gemara to be obligating payment if one was forced to damage property, even though the damaging was done permissibly.
A compromise view put forward by some modern-day Acharonim is that in essence (for some reason) theft is forbidden even to save lives. However in a case where the other person would be obligated to give the thief the money anyway (to save his life), it is permissible to take the money without permission.
With all that, it's hard to say that stealing would be prohibited. However one would clearly be obligated to pay back, and it would of course be forbidden to put oneself in such a situation.