PTC resistor, by any other name...
 

My refrigerator died. It was Friday evening when I took notice,
and transferred half the contents to coolers with ice, ate as much as wouldn't
keep without freezing, and tossed a lot of the rest.

Tracked down the symptoms, and it's undoubtedly the motor-start
PTC resistor unit that emitted its magic smoke. Pulling
things apart was amusing (cramped kitchen, with a new island
in the midfloor, consisting of coolers).

So, there wasn't any circuit diagram on the back panel,
but plenty of internet mumblings and charts (and videos)
on the issue. The covers came off and revealed a boxy
thing that takes electricity in (two terminals) and sits
on two prongs that emerge from the compressor motor.

It's a 'motor protector', 'motor starter', 'thermal relay', 'overload kit',
and half a dozen other names also are sometimes applied.
The refrigerator manufacturer has discontinued (and/or is
just out of) this part, but a different manufacturer DOES still
have their 'kit' that the local store can get me, probably with
a day's delay. Klixon made this unit, not the refrigerator
manufacturer, and has gone through three part-number-revision
changes (from 8EA40x to 8EA4Bx to 8EA14Cx...). It took
an hour on the internet to find enough info to confidently get a part
number that isn't unobtainium.

So, here's the greater issue: my local supplier is an authorized
repair center for the refrigerator's manufacturer, so they can
only ever recommend the certified replacement part or kit. How
many people throw away a refrigerator when a socketed PTC resistor
fails? This is a positive-temperature-coefficient "switching"
component, which kinda cooks itself as part of normal operation,
so they fail quite often.