A little TIM can leak or cook out before it fully "cures" ... especially if too much is used (probably the most common blunder). Solder-like TIMs can behave like solders when heated, flow towards heat and get sucked or pushed by capillary action between mating surfaces.
All TIMs are thermally conductive but not all are electrically conductive - if your TIM isn't electrically conductive then it wouldn't "short circuit" anything. CPU voltages are low enough that they couldn't puncture the plastics or the onboard solder mask, so the only real concern is TIM on the silicon "filaments" or TIM in the socket pins. A big mess with lots of liquid spilled on board would be a concern since it could bridge solder points or even seep into the solder balls under BGA parts.
If it's gotten into the socket or other places it shouldn't be then it could be interfering with proper mechanical fit. If it's electrically non-conductive then it could actually be preventing normal electrical contact inside a CPU pin (which wouldn't "short circuit" or burn/explode anything but would inhibit normal part functions). Tolerances and mounting pressures on CPU coolers are pretty tight and Intel didn't actually design the thing to be de-lidded in any event, lol.
The only guaranteed way to get it all out from inside tiny pinholes or under surface parts would be immersion in an ultrasonic cleaning machine (of the specific sort used by repair technicians). Otherwise try wiping and scrubbing and air-blasting what you can and hope no damage was actually inflicted by the leak.
I don't expect the CPU socket would have any short-circuit protection built into it, beyond perhaps some teeny tiny FIVR-style diodes (as likely to be in the CPU package as in the socket) ... since the motherboard just wasn't designed for anything other than a socket-compatible CPU to be plugged into that socket. Stuff like power inputs, USB ports, network connectors, and maybe even PCIe slots might have ESD shielding and electrical hardening since you never know what sort of electrical junk people will stick into these holes, but the CPU socket doesn't normally need such failsafes (they'd likely just add cost and complexity while slightly impacting performance).
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