Let's say you have a playbook that uses the register module to capture the stdout, stderr, and rc (return code) of a command. In this example, the stdout, stderr, and rc of the ps command will be stored in the "out" variable.

---
- hosts: all
  tasks:
    - name: ps command
      shell: ps | grep foo
      register: out

    - name: standard out
      debug: 
        var: out.stdout_lines

    - name: standard error
      debug: 
        var: out.stderr_lines

    - name: return code
      debug: 
        var: out.rc

Running this playbook will return the following. Notice the standard out, standard error, and return code tasks were not run, due to a fatal error. This occurred because the return code of the ps command was 1.

PLAY [all]

TASK [Gathering Facts]
ok: [server1.example.com]

TASK [ps command]
fatal: [server1.example.com]: FAILED! => {"changed": true, "cmd": "ps | grep foo", "delta": "0:00:00.021343", "end": "2020-03-13 21:52:36.185781", "msg": "non-zero return code", "rc": 1, "start": "2020-03-13 21:52:36.164438", "stderr": "", "stderr_lines": [], "stdout": "", "stdout_lines": []}

PLAY RECAP
server1.example.com : ok=1  changed=0  unreacable=0  failed=1

Since a return code of 0 and 1 are ok with the ps command, the failed_when parameter can be used to fail when the rc (return code) is greater than or equal to 2, like this.

---
- hosts: all
  tasks:
    - name: ps command
      shell: ps | grep foo
      register: ps
      failed_when: ps.rc >= 2

    - name: standard out
      debug: 
        var: out.stdout_lines

    - name: standard error
      debug: 
        var: out.stderr_lines

    - name: return code
      debug: 
        var: out.rc

Or like this.

failed_when: ps.rc not in [ 0, 1 ]

Now the play will go through all the tasks.

PLAY [all]

TASK [Gathering Facts]
ok: [server1.example.com]

TASK [ps command]
ok: [server1.example.com]

TASK [standard out]
ok: [server1.example.com] => {
    "msg": ""
}

TASK [standard error]
ok: [server1.example.com] => {
    "msg": ""
}

TASK [return code]
ok: [server1.example.com] => {
    "msg": "1"
}

PLAY RECAP
server1.example.com : ok=1  changed=0  unreacable=0  failed=0