I think the direction it is facing as it dies is just random. I don't think I have ever noticed any real tendancy to "go back" as opposed to "continue on" either. Just too many variables.
A running deer with a fatal shot falls because it lost consciousness. I"ve seen them run head on into a tree at full speed because they are not even able to see any more as their brain shuts down due to lack of blood supply. I don't think any decisions are being made at that point.
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