A TRACON Controller reported they assumed a descending aircraft was descending via a published procedure but they were not and descended below the Minimum Vectoring Altitude.

Narrative

Pilot checked on my frequency around 10000 to 11000 ft. and said they were descending to 6400 ft. They were right over the top of a descend via arrival so when they checked on descending to 6400 ft. which was weird I made the assumption they were descending via an arrival; which would be safe with terrain. I was wrong. The pilot descended to 6600 ft. in a 072 ft. MVA. By the time I noticed; he was exiting the 7200 ft. MVA and entering a 6200 ft. MVA. The 6200 ft. being safe for his present altitude of 6400 ft. thus I did not issue a terrain safety alert. At that point I vectored him toward destination and told him to maintain 6200 ft.And I inquired what he was assigned previously. Pilot said he was cleared by previous Controller 'direct ZZZ VOR and assigned 6400 ft. which doesn't make any sense of why the previous Controller would do that. An assignment of 6400 ft. would drop below at least two higher MVA's. Not sure how this all began; but it was not safe. I take part in the blame; I should have inquired; instead of assuming. I take part in the blame; I should have inquired; instead of assuming. I'll eliminate assuming in the future. I'm typically good at that.