Can bone grow back on its own?

It sounds like you lost bone in the lower anterior section of the mouth.  The boney ridge that supports the teeth in this area is generally very narrow as compared to other parts of the mouth.  Many people have thin ridges to start and loose teeth means some of the bone around the sockets has resorbed.  You are also right in thinking that further bone loss has probably occurred since the teeth were extracted.  The bone typically does not grow back in this area as the underlying support from the socket is missing.  Bone grafting is possible in this area but not as predictable as other parts of the mouth.  All this does not prohibit you from placing implants however but the crowns will end up being very long as the surgeon will have to engage the jaw bone itself which is further down.