A TRACON Controller reported they accepted a handoff on an aircraft then noticed the previous sector left the aircraft at an altitude below the Minimum Vectoring Altitude.

Narrative

I had just sat down at ZZZZZ. The Controller being relieved briefed me that 'Aircraft X is talking to departures' and I observed Aircraft X tracking about a 290 heading; which is a pretty vanilla heading we issue for ZZZ Departures and then let the Departure Sector turn northbound aircraft at their discretion through/under the ZZZ1 Departure flow. About 5 minutes later; I notice Aircraft X; now a full green data block on my scope; has a red flashing 'CLIMB' in line zero of the data block. The Aircraft X had flown into a 5000 ft. MVA and was level at 4000 ft.; heading towards terrain that is at least 3600 ft. This immediately caught my attention and I yelled over to the combined departures scope (3 scopes down from me); 'Hey! Climb that Aircraft X!' I immediately transmitted on my frequency to the Aircraft X to turn north and climb to 5000 ft. immediately just in case he was sitting on my frequency. I again immediately yelled for Departures to climb Aircraft X.The Departure Controller seemed unaware of the situation and mumbled 'he's not on my frequency'. Then a few seconds later the departure Controller tried Aircraft X again; but by this time Aircraft X seemed to have turned himself to parallel the rising terrain but remained level at 4000 ft. It is my opinion that the Controller working the Departure Sectors had fallen asleep. Another Controller had mentioned about an hour later that the Controller working the departures at the incident time had very red eyes in the break room. I would not have done anything differently in this situation that would have prevented this occurrence. To be clear I observed this event and was not the Controller working.