This could be performed if the incident management profile is being modified.
For example in out of the box (oob) system if falcon needs to edit close tickets then please follow the below steps :
1. Login Service Manager asGo to Navigator -> system administration -> Ongoing Maintenance ->Operators
2. Search by falcon
3. In the record, the incident profile is “sysadmin”
4. Click find button besides incident profile
5. The above will open sysadmin incident management profile.
6. There is one option called update when closed
7. Check this option, then the operators with sysadmin incident management profile will be able to edit some fields of the close ticket.
It can be done for other incident management profiles also.