A mutlaq expression refers to an unrestricted member, while a muqayyad expression adds a valid quality or condition. Mutlaq does not mean “every member”; that concerns generality. A stated qualification cannot simply be ignored.
رَقَبَةٌ
A slave.
رَقَبَةٌ مُؤْمِنَةٌ
A believing slave.
The oath and accidental-killing expiation passages illustrate unrestricted versus qualified terms. Interpret each in its own context; a condition is not carried from one text to another without valid grounds.