What happens to camera when you hit the shutter count limits?

The shutter count limit is just the expected number of actuations that the shutter will be able to make before it dies. This doesn't mean the shutter will die right at that number though.

Let's say for example, that the expected shutter life of a camera is 150k. It's entirely possible that the shutter could still be functional after 300k actuations. It's also possible (while unlikely) that it'll randomly die after only 200.

The shutter count is similar to miles on a car with how a car might have an expected number of miles it'll last before the end of its life, but definitely can die long before or after that expected mileage.