Olives are very hardy plants indeed. They are perfectly adapted to the Mediterranean climate of long hot summers and cold winters.
Below is a shot from an adjacent grove where the owner is reducing the number of trunks from 3/4 down to one but has not yet removed them and so there remains a stump a couple of feet high which you can see is sprouting new growth.
A lot of other plants would not survive this kind of treatment but the olive continues on.
We have here at Casa Margherita pruned some trees by chainsawing a trunk back to a metre off the ground and then developed the re-growth into the classic wineglass shape. After 3/4 years the tree will be bearing fruit again.