ATC reports an aircraft read back a wrong altitude; resulting with the aircraft being below the MVA. ATC issued a low altitude alert and crossing restrictions for the approach. Aircraft landed at the destination airport.

Narrative

Aircraft X was base turned at 5200 and then given PTAC with 5200 until established on the localizer. Aircraft X read back 4000 until established. The MVA was 5200. Read back was missed due to center calling repeatedly on the shout line trying to pass a pirep. As I disseminated the icing pirep to other aircraft I observed a low altitude alert on Aircraft X as they entered 4700 MVA at 4000 and issued low altitude alert; MVA; and then crossing restrictions for the approach. I had a stand alone Supervisor behind me that also did not hear the bad read back. Aircraft X had went around prior to this approach and I was already giving my full attention to them as this was their second approach. I had vectored them to give them time to run through their checklist and I was paying attention as I expected another missed approach could be possible. While I understand the importance of a heavy icing pirep; we do not have coordinators or D-side at this TRACON. Aircraft X should call us and be patient; we will answer as fast as we can while keeping the traffic safe. If I cannot answer then any available oversight should be helping.