What does an inductor's current stabilize to in DC?
At DC an ideal inductor behaves like a short circuit. The voltage across it is 0 but the current through it depends on the specific circuit it is in. In the case of your circuit the DC current is evidently 6.5mA.

An ideal capacitor has the opposite behavior -- it is an open circuit at DC. The current through it is 0 but the voltage across it depends on the specific circuit it is in.