sorry brain fade. Should have said
.... later in summer/autumn, after flowering use the bulbils and lastly the bulb. When you dig out the bulbs, there are smaller bulblets hanging off the bulb. These vary in number, they are encased with a light brown, hard skin with a sharp point. Leave these and they will eventually grow a new Babington leek. Elephant garlic have similar bulblets, which can be used to grow more elephant garlics. They sprout quite slowly, sometimes take two years to sprout. I took some bulblets out last year and put them in a pot. Only one has sprouted, the others are biding their time.
As Babington leek is a permanent bed plant and not part of a rotation, these can just stay in the soil. I tried to rotate my Babington leeks and ended up with 3 spots in the garden where they come up as they like.
Even if you think they have all been dug up, it is very likely that they will sprout up again, which fits with your story of livestock trampling and eating the lot and still, Babington leek found a way to resprout, either from the bulbs or from the bulblets that are hanging off the bulbs.
