A TRACON Controller reported an aircraft descended below their assigned altitude and flew below the Minimum Vectoring Altitude.

Narrative

Extreme weather was impacting the sector and all frequencies were in speaker due to lightning pops in headsets. Aircraft X was holding waiting for weather to improve and had 10 minutes left prior to them needing to divert. I advised Aircraft X that we had a window of improving weather and they decided to try RNAV Y Runway XX at ZZZ. I issued heading 300 descend and maintain FL060 vectors for ZZZZZ. I thought I heard a proper readback but after listening to the tapes it seems the pilot may have readback FL030. I was then on a line with ZZZ [Center] for a pointout. As soon as I got off the line I noticed Aircraft X rapidly descending through the MVA of FL052. I immediately told Aircraft X they were below MVA and to climb a maintain FL060 immediately. They didnt immiediatley resond so I issued it again stating low altitude alert. Aircraft X responded as instructed and stated that they thought they were cleared to FL030. I notified the supervisor of the situation and they said they would have Tower issue the a warning when the aircraft was safely on the ground. The radar nor the pilot TCAS went off during the event.I recommend staying vigilant for myself my supervisor and pilots for hearback/readbacks esspecially in situatings of bad weather and equipment problems. The pilot should have verified a clearance they thought was at FL030 since the approach they requested at ZZZZZ starts at FL052. Also since the frequency was hard to hear in speaker with lighting pops I should have verified the readback when the altitude wasn't completely understandable from the pilot.