A TRACON Controller reported an aircraft encountering icing could not maintain altitude and descended below the Minimum Vectoring Altitude.

Narrative

I was working ZZZ's radar position with all sectors combined to one because traffic was low mainly due to bad weather in the area. There were low ceilings throughout the airspace (around 800 ft. at ZZZ; ZZZ1; ZZZ2) and reports of rime icing mainly at 5000 ft. and higher. As I was scanning the scope I suddenly noticed that a target that ZZZ Center was working at 9000 ft. had descended to below 8700 ft. and begun flashing to me. I assumed there was an issue with the aircraft as an amended flight plan printed off and showed ZZZ as their new destination. After checking on the frequency; and me briefly coordinating with ZZZ Center the pilot advised that they were encountering rime icing and were descending. Based off of earlier PIREPs I believed the icing would improve around 5000 or 4000 ft. I ultimately issued 4000 ft.After a short time; I noticed the aircraft still had a rapid rate of decent and was below 4000 ft. The MVA in that area is 3000 ft. so I asked the pilot if they could maintain 3000 ft. and told them that 3000 ft. was my lowest usable altitude. The pilot responded that they would try but were still getting icing. Unfortunately the pilot was unable to maintain 3000 and continued to descend below my MVA. At this point I started communicating with the pilot in plain English because I really needed them to understand that my MVA was 3000 ft. which meant that obstructions were around 2000 ft. Once the scope created the low altitude alarm; I started to issue a Low Altitude Alert but before I could fully finish the full phraseology I said disregard. I'm not sure why this happened in the moment but it was probably because myself and the Supervisor were discussing the best course of action; and I wanted to finish hearing their thoughts before transmitting more in case they didn't agree with the current transmission. Ultimately I went right back to the pilot and issued an immediate climb. Proper phraseology was slightly broken up; but I feel the important info got to the pilot. The lowest I saw the aircraft was around 2000 ft; and because I knew this was a situation; and the pilot was also trying to prevent a stall situation I used more plain English to simply tell the pilot to maintain above 2100 ft. no matter what to avoid whatever terrain/obstructions might be there. At that point it was clearly a priority; especially since the bases throughout the airspace were so low. After a few minutes the pilot seemed to recover and start a slow climb; so I thought it best to leave the pilot be and waited a few more minutes to confirm maintain 3000 and asked if they were ready for vectors to the ILS XX at ZZZ. The pilot ultimately landed safety after an ILS approach; and also advised that they lost their airspeed indicator during the event. In summary; I had to use plain English and issue a 'soft' clearance to tell this aircraft to maintain what I knew to be an altitude clear of terrain and obstructions; but it was below my MVA. Additionally; by low altitude alert phraseology was broken up over the course of the event; but I feel it still conveyed the proper information to the pilot in a way that didn't overload them. I hope the pilot of the aircraft had the proper weather forecast and knew the conditions they would be experiencing. This weather system was forecasted several days in advance. Not taking a plane without the proper de-ice and anti-ice into this weather would have prevented this situation. I am glad that the pilot took action when they did.