Saving the vine might be possible. The vine needs to form new subterranean roots that extend into the soil to survive, however. It’s quite easy to stimulate an ivy cutting to produce new roots with the aid of rooting hormone, which can be bought in garden supply stores.
The English ivy in my garden started from cuttings treated with a specific rooting hormone as part of a university project. The instructions for obtaining suitable cuttings from a vine and using rooting hormone might be present on the product package, and can also be found on various websites.