How terraform handles the crash?

Terraform maintains details of all the resources created during “terraform apply”, inside tfstate file. The file needs few time to be updated. But if there happens a breakdown, such that our instance is created in aws but tfstate file is not updated, how can terraform recognize the change and update the tfstate file ?

You would manually investigate the issues and then correct the state file accordingly. This could be using terraform state rm & terraform import for example.