A Center Controller reported an aircraft encountering icing descended below the Minimum Vectoring Altitude.

Narrative

Aircraft X came to me from ZZZ Approach reporting light icing. I had informed ZZZ approach that due to my MIA's I would not be able to turn or descend this aircraft until the vicinity of ZZZ1. I let the pilot know I would descend them to my lowest usable altitude of 8000 ft. in less than two minutes. Shortly after; Aircraft X showed descending to 8700 ft. in the 9000 ft. MIA block. I asked them to verify level at 9000 ft. and the altimeter; as this commonly happens in this area as they change altimeters. They said they were unable to maintain their altitude due to icing. I called a low altitude alert and told them to maintain 9000 ft. if possible.Once they entered the 8000 ft. block I descended them to 8000 ft. They were supposed to turn south; which would keep them clear of a neighboring 9000 ft. block; but they did not make the turn. I turned them XXR at first; then eventually put them on a 150 heading when they turned too slow to miss the block and called a low altitude alert for the 9000 ft. block they had turned in to. At this point they were still slowly descending and it became clear they needed to land now. I offered them ZZZ2; as it was the closest airport; and they accepted. I called ZZZ3 and told them the situation and coordinated 7000 ft. altitude and 090 heading to get them to ZZZ2. The aircraft was still descending so I asked them to try to maintain 7000 ft. for the next sector and called another low altitude alert. I put them on the 090 heading and eventually changed them to ZZZ3's frequency. The pilot was clearly in distress so I did not ask them the type of icing while I had them; but later called ZZZ3 for a report and was told the icing was severe mixed icing. I put in the PIREP and informed that other aircraft in my sector that may be affected by this.We had no other reports of icing in this area today; so there was no way of knowing it was going to happen. In the future I could inform ZZZ approach perhaps to have the aircraft return to ZZZ if they were getting bad icing at 9000 ft. my lowest usable altitude.