In the USA, the grid transmits power at/around 60Hz. How big of a frequency deviation can the grid handle before relays trip and cause a blackout?
Short answer: The range is usually held within ±0.5%, so its from 59.7Hz to 60.3Hz for a 60Hz grid.

Long answer: Frequency is regulated tightly because it's how the overall load in the grid is controlled. If there's a runaway to lower frequencies, that usually means there is a short-circuit near a major power station or hub. So that will drop out soon. Then there usually is a runaway to higher frequencies because of the dropped load. So things escalate very quickly if the grid has many gigawatts power stations. And you don't want that.

In weak grids on the contrary, the frequency may swing much more. Eastern European countries typically allowed 47Hz to 53Hz. That's acceptable if there's only a few power stations and a few big consumers. The same for emergency generators and isolated grids on islands.

What limits the frequency downwards is power conversion in transformers and AC motors. The lower the frequency is, the lower the primary voltage needs to be not to overexcite the iron parts by the magnetic fields. So a substantial frequency drop has to be accompanied by a voltage drop too, and that's what is done in weak grids to allow lower frequencies.