At a moment in time, the status of a process is one of four values:
PAUSED for editing
DONE (in which case the process result is either COMPLETED or STOPPED)
A process owner MAY delete a process whose status is either DRAFT or DONE.
A process owner CANNOT delete a process whose status is either IN_PROGRESS or PAUSED.
That is, if you want to delete a process that has been started, you MUST first EITHER:
stop the process OR
complete the process.
If the process owner tries to delete a process whose status is IN_PROGRESS or PAUSED, the result will be a HTTP 403 error with detailed error code of 1403010.
This feature is meant to give a running process a kind of "delete protection", to prevent a process that represents an important ongoing business activity from being accidentally deleted.