The 105 left shifters are capable of either 2 or 3 chainrings; they have three chainring positions built into them. Shimano now sends a warning label attached to some of these sorts of shifters. It basically says that if you only have two chainrings, don't force the lever into that third position or you may break it.

If that's what happened in your case, then , especially if you weren't briefed on this potential problem. Those shifters are quite expensive, so here's hoping you really did just break the head off the cable, but you'd probably have noticed by now if you had, because the cable housing wouldn't stay in the lever anymore.