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

Narrative

During the event; I was working as a radar controller for West and East combined; responsible for all arrivals and departures. Aircraft X was handed off from Center IFR climbing to 070 MSL. Once I received communication with Aircraft X; I descended Aircraft X to 050 MSL and asked them what approach they wanted. Aircraft X eventually decided to accept the GNAV RWY 20L approach since they were parking on Location A of the airport. During the time it took for them to fly inbound from; I had Aircraft Y inbound 10 NM from the west get the field in sight at 042. I informed Aircraft X of this and offered to descend them if they would like to go for the visual approach to RWY 20L. Aircraft X decided they would accept a visual approach; take lower; and even cancel IFR once they got closer. Aircraft X started descending on their own out of 030 MSL in the 029 MSL MVA 1.5NM from the 023 MSL MVA. I did not catch Aircraft X's altitude until 10 seconds later because my attention was on other aircraft at the time. Once I realized Aircraft X was descending; I issued them a low altitude alert. Aircraft X responded they were VFR. I responded asking Aircraft X if they would like to cancel IFR. Aircraft X confirmed IFR cancellation. I relayed to Aircraft X IFR cancellation received; gave them a pattern entry; and transferred them to FAI Tower. I believe this event occurred due to the pilot's expectation they would go VFR once they got clear of clouds.Suggestion: I recommend controllers keep up their scans of IFR aircraft's altitude; especially those who are not 'regulars' at your airport. I think pilots should follow instructions for altitude restrictions and request cancellation of IFR before they alter from their altitude restriction.