140820-1000 EDT
GITRDUN:
You did not indicate the year of the machine.
Almost certainly these are pullup resistors. Because they are 10 K and in a multi-resistor package. I suspect it was an early machine before they isolated the logic gates from the limit switches with optical couplers. In those machines pullup was to +5 V. This resistor is between a logic gate input and +5 V, and the limit switch pulls the logic gate to 0 V when closed. Max power dissipation per resistor is 25/10,000 = 2.5 milliwatts. That resistor will never fail from the normally applied power. To have a high voltage applied to the resistor that would cause failure almost certainly would damage the logic gate. Is there other protection at the logic gate input? I don't know.
To damage a 10 K 0.25 W resistor will probably require 1 W for milliseconds. To produce 1 W in 10,000 ohms requires 100 V.
This was not a good design for several reasons, but we have never had a problem in this area with the our early machines.
Were this a newer machine with the optical couplers, then the resistor would need to be much lower. In this case the pullup voltage is +12 V, and an optical coupler, like the 4N35, would probably be driven by about 10 mA requiring about 1000 ohms for pullup.
Resistors and transformers run below their maximum ratings typically have very long lives. Easily more than 50 to 100 years.
This failure does not seem to fit the pattern you have generally described. Your description implies that the failure did not occur while the machine was powered, but may have occurred at power down.
.