If the user is eligible for the Task Group corresponding to the Task, it is not even required to assign that Task to the user.
User can execute the Task even without assigning the Task. While executing the task, internally the task would get assigned to that user.
To give a better understanding,
Let us consider a task ‘Task001’ is with Task Group ‘R02’ and four users User01, User02, User03, User04 are eligible for the Task Group ‘R02’.
Any of the four users can pick and execute the task even without assigning. If User02 has executed the Task, then it will be automatically assigned to User02 internally(Task_Hdr.Owner_User_Id would get updated with that User).