I got a Keithley 2000 multimeter, and as usual the first thing I did was to test it.
Builtin self-test ran through most of cases without issues but failed with 600.1, 600.2 and 601.1.
With a little research I found out that those errors are related to amps/ohm tests, and a little later I found out that one of the common causes is broken relay (K103) – NEC EA2-5NJ.
I took the device apart and probed the relay, comparing the result with other two relays.
It should have pins 2,3 and 8,9 shorted when off and 3,4 with 7,8 when on.
My relay has all the pins 2,3,4,7,8,9 shorted together – that is definitely not desired.
I ordered a new relay from Mouser and when it arrives I will replace it and see if that solves the problem.