There are a number of ways to handle fatal errors.

• Use fail to end a play and return "failed" 
• Use the --check command line flag to run the playbook in a dry run mode
• Use check_mode to determine if any fatal errors would be returned
• Use failed_when to continue based on the task return code
• Use ignore_errors to ignore errors returned by a task (this article)
• Use meta: clear_host_errors to clear errors so that subsequent tasks are run
• Use meta: end_play to end a play for all hosts
• Use meta: end_host to end a play for certain hosts and return "skipped"
• Use block rescue always to run tasks even after a fatal error is returned
• Use stat to determine if /tmp/foo.txt exists and the when parameter to skip the lineinfile module if /tmp/foo.txt does not exist.
• Use stat to determine if /tmp/foo.txt exists and then use the file module and the when parameter to create /tmp/foo.txt if the file does not exist

There are a number of different Ansible tasks that can cause a playbook to cease execution, typically when the return code of a task is anything other than 0. As an example, let's say /tmp/foo.txt does not exist, and you attempt to append "Hello World" to /tmp/foo.txt using the lineinfile module.

---
- hosts: localhost
  tasks:
  - lineinfile:
      path: /tmp/foo.txt
      line: Hello World

  - debug:
      msg: "I am here"
...

Invoking this playbook will return fatal, like this, and the playbook would cease to move onto the remaining tasks.

fatal: [localhost]: FAILED! => {"changed": false, "msg": "Destination /tmp/foo.txt does not exist !", "rc": 257}

Here is how the ignore_errors parameter could be used.

---
- hosts: localhost
  tasks:
  - lineinfile:
      path: /tmp/foo.txt
      line: Hello World
  ignore_errors: true

  - debug:
      msg: "I am here"
...

Invoking the playbook should now return the following. Notice the lineinfile task contains ...ignoring and the debug task is processed and the play recap has ignore=1.

TASK [lineinfile] 
fatal: [localhost]: FAILED! => {"changed": false, "msg": "Destination /tmp/foo.txt does not exist !", "rc": 257}
...ignoring

TASK [debug] 
ok: [localhost] => {
    "msg": "I am here"
}

PLAY RECAP 
localhost                  : ok=3    changed=0    unreachable=0    failed=0    skipped=0    rescued=0    ignored=1