I noticed this almost as soon as I came here in August. In fact, I never ended up setting up voicemail on my phone - not sure the little 10-leva thing even has the option? At first I was like "okay, fine, I can get used to this." Except eventually I realized that if someone is calling for something important (i.e. the lawyer's office who was helping with my lichna karta), and they can't or won't leave a voicemail, they just keep calling. And calling and calling. So if you're sleeping/napping/taking a minute away from the world/your phone, you have to give it up and answer the phone. Or turn it on silent, but then of course, you could miss said important information. Or unimportant, depending on the situation.
It's interesting the way this culture of cell phones/ non-culture of leaving messages makes for an annoying assumption that one ought to be accessible by phone 24 hours a day. For most cultural differences between the States and Bulgaria I can fairly easily say "mm hm, I can definitely see how you would look at it that way," but I've always had a hard time with this one.