Okay, agaIn, I'm no expert on this material, but as I was saying earlier, it's a very sloppy mortar job. Also, as mentioned..... ALL things expand and contract. Whatever rate that might be, everything does. Upon further looking at the 3 pictures and using normal deductions, it looks as if the sign itself was expanding and the rock/stone/mortar confinement is too small, thus forcing the lesser material to bend, then shoving it out. The same kinda deal when one puts aluminum or vinyl siding in and it needs enough room to expand, but not too much that it bows. Same as a electric sign face within the confines of the cabinet. Something will always give when push comes to shove and in my novice opinion, that's what happened. The hole was too small. I'll bet ya 10 to 1, the sign fit too snuggly in there and whoever installed it, never considered it.
Always..... always leave some breathing room.