Hello yes  your teeth  can be saved.proceed with 're rct .takes bit more sittings and special  medication  .

Sometimes the problem does get cured by retreatment and it shall be the first line if treatment. In worst case your might need to undergo an apiecetomy. That is a surgical removal of the infection from the root area. Minor surgery done on a dental chair under local anasthesia itself . But first attempt is to do a re rct by a specialist