The olive tree is an amazing plant. It can live through virtually any condition, though they need drained soil and they do not like serious frost. When faced with limited water, an olive tree will simply slow down and not produce any olives, but it will come back in later years. An olive tree planted in a lawn, where it has ample water, will grow quickly and produce a large harvest of olives.
There was a very deep freeze in 1985, which killed much of the olive tree wood above ground in Tuscany and Provence, but the trees survived. While there was no harvest in northern Italy and southern France for at least two years, southern Italy's trees were much less affected. In fact, that frost let to the modern grown of olive oil production in Puglia. Today, the trees in Tuscany have been pruned to promote the wood that grew from the roots. We have seen trees where the you could drive a car through the middle opening. If you ever see a photograph of an old olive tree with a single (fat) trunk, it is probably from Sicily, or North Africa.