Attention!
SAP BASIS Administrator: The more rights in the system the more responsibility.
additional verification, additional call to the user and additional backup will not be superfluous
Symptoms
Symptoms of zombie processes
Transaction - SM50 (Work Processes of AS Instance)
WP Status - "Running" and Time - <Abnormal values>
For example Time on screen
3296541 seconds -> approx. 38 days (absolutely abnormal values)

Addition verification:
Transaction - SM04 (User Sessions of AS Instance)
Verification of abnormal situation - Session for the user from previous screenshot not exists in the list
Prerequisites
You try to execute
SM50->Administration->Work Processes->Cancel with/without core
but no results
Resolution for Windows
Open Powershell as Administrator
Get-Process -id <Process ID from SM50>

Stop-Process -id <Process ID from SM50> -force
Resolution for Linux
Logon as the root user
ps aux | grep <Process ID from SM50>
kill -9 <Process ID from SM50>
Conclusion.
SAP BASIS Routine task with examples from real life was provided