How do you estimate the probability of failure in this case?
The bigger problem is there's no such thing as #16 wire that is certified for use in AC mains wiring inside houses.  Look at the NEC Chapter 3 wiring methods, which enumerates each and every allowed wiring method.  All of them call out wire or cable types that do not exist in 16 AWG.
So if 16 AWG is being used, someone is doing something illegal.

Using 16 AWG cordage as a substitute for permanent wiring (NEC 400.8)
Using 16 AWG speaker, automotive, etc. wire not approved for AC mains (NEC 110.2).

The only exception is wiring that is present inside appliances.  Those follow a different Code body called the UL White Book, authored and maintained by Underwriter's Laboratories.  Because of the very short distances inside appliances, and dependent on the wires' ability to cool inside the machine (or alternately approved use of high-temp wire where it has no chance of burning a user), it is possible to use smaller wires inside an appliance.
There's another Code out there called NESC which applies to utility company wiring outdoors (i.e. their side of the weatherhead).  They can overload wires in ways NEC does not allow, but remember, those wires are not inside a structure.  And the electric company has financial incentive to keep those wires cool, since it's on their side of the meter, so they pay for heating the great outdoors :) They also have direct real-time observation of the load level on those wires due to smart meters, which can be programmed to &quot;phone home&quot; if draw exceeds safe limits for the service drop.  Often when they upgrade someone's service, they will not upgrade the drop wires, betting that the customer won't actually use all the service they have, until the meter tells them otherwise.