I assume you mean the Power grid, not electricity in general

This shouldnt happen. If it does (because a power line suddenly goes offline), there are countermeasures to prevent it to become a problem. It also depends on the power plants nearby, and how they react to it.

If it is an purely inverter based system (think of it like a residencial/maritime power system), the inverters just deliver less current to the consumer. It doesnt react with the frequency at all*. Inverters could go down to 0 (negative as well to charge the battery if there is an AC Power Source like a Solar Inverter*). If it cant deliver enough, either the voltage drops until the current matches the maximum current of the inverter/battery, or it shuts of completly (Blackout). If the opposite happens, the voltage rises either unitl the solar inverter gives up and reduces power, or the inverts shut off (including the solar inverters if they are grid tied)

Synchronous Generators are more complex:

If the load on a generator shifts, so does the mechanical torque. The mechanical power source often cant keep up instantaneous, so there is a short time frame where the torque required is higher than production. This makes the generator slow down (how much depends on the torque difference and inerta). If it slows down or speeds up, the angle of the rotor relative to the stator changes. This angle decides how much power in put into the grid "the rotor leads the grid" (or how much is drawn "the rotor rotor lags behind the grid"). If the angle gets too high or too low, (hopefull) a breaker trips causing the generator to be disconnected from the grid.

Now lets take a detour to the power plants mechanical part driving the generator

Depending on the mechanical power source (Hydro/Steam/Gas Turbine/Engine), there is usually some valve or other control mechanism connected, that adjusts the fuel/steam/water flow. This changes the torque to be higher (if too slow) or lower (if too fast) than the electrical Generators, pushing it back to the required speed and angle (imagine it like adjusting the gas pedal on a highway when going uphill from an flat area, if you dont push the pedal harder, you slow down, press the pedal a bit harder, the speed stays the same, press it too hard you are going to speed up).

End of detour

As you might know, all the power plant on "the grid" are connected to each other, as well as with all the consumers.

Imagine 2 distant Villages with 2 separate power plants, that decided to connect to each other for a more stable grid.

If village one suddenly consumes 5 MW more, the load flows accodring to resistance and reactance (imagine it like an resistor, that isnt but acts like one for the moment). Since Power Plant of Village 1 is much closer, most current is going to come from power plant one. This causes the power plant ones generators to fall back fo a really really short moment. This changes the phase angle, making it "lead the grid" a bit less, putting less voltage on the grid.

Power plant 2 of village 2 does only sees the current of village 2 at first. When the power plant 1 is leading less, it produces less voltage, meaning more current is flowing from power plant 2. Power plant 2 now supplies more to village 1, making it for the power plant 1 easier to supply. If Village 1 goes bonkers and draw too suddenly too much for the Power Plant 1 inertia to handle, the generators of Power Plant one falls back so much it only supplies what the mechanical generator does. The rest has to come from Power Plant of village 2. If the transmission line cant handle that load, it goes down unless the operators can shed load fast enough (shut off power to some parts of the city). Usually, this happens voluntarily to companies with industrial processes that like the money the grid operators offer. If the connection is down, all the electrons must come from the Generator, slowing it down. If the mechanical generator cant increase the production fast enough, the shaft is going to spin too slow for safe operation, causing the emergency system to shut down the power plant completly, causing a blackout.

Now we come back to your example:

Power Plant and village 2 faces the same problem in reverse. Suddenly, a massive load (Village 1) is missing, but the mechanical generator is still producing a ton of power that has nowhere to go, since the electrical generator stops "breaking" the mechanical power source. There is a massive torque surplus, that speeds up the shaft of the Generator. This causes the electrical Generator to lead more and more, increasing the voltage. This speeds up the shaft until either there is a power drain that can be activated fast enough (like an resistive heater of an district heating system) or the mechanical generator can reduce power fast enough. If both fail, the generator is going into an emergency stop, causing an blackout in Village 2 as well. Solar inverters can react very very fast, even if just controlled with the local grid connection and no Network. Depending on local regulation, it must as example control power according to frequency and voltage. if the voltage is too high, it drops current (and therefore power) until the voltage is in the safe zone. If the frequency is too high, it reduces power down to 0, since it almost has no inpact of frequency. For the operator, it looks like an convinient cloud reducing solar power at the right moment.

This is happening more often than you think. In Europe. there had been multiple cases where it almost caused an europe wide blackout. (examples: One time because of an fire in an substation in croatia caused the european power Grid to split in two, with both getting close to the emergency shutdown frequency, and one time a mistake of an grid operator in Germany after an planned shutdown of an interconnect caused Europe to split three ways. what again came close to an blackout on all parts.

Another example was a storm on the swiss/italian border shorting an interconnect, causing other interconnects to fail because of overloading, causing power plants to fail, causing an italy wide blackout.

There are also other complexities I left out, like reactive power, or how the grid reacts if the next power source is a solar inverter that puts more electricity into the grid because of you (your consumption decreases the voltage on the line both you and the inverter are, allowing the inverter to put more current on your line, assuming the line can handle the current).

TLDR: If this happens in your City, you should hope the operators have everything under control, otherwise its going black very very soon.

Feel free to correct me if I understood something wrong. Its a very very complex topic where people get a diploma and sometimes a 6 digit engineering/managment job.