Can be the estimated
Mean Absolute Error (MAE) equal or more than
1? If it is possible (which it happened to me), when it happens and what is the reason?
Of course an absolute error can be greater than $1$. The "absolute" says you are calculating a difference.
When it happened to you it probably means just that the data are very widely spread out.
If you are still puzzled by anomalies in your data you should probably post them in a new question, show us your analysis and what bothers you.