What happens if my GPA drops below the department requirement?

Every school is different, but generally, this is how it works (in the U.S.).
You get into college, but you are not OFFICIALLY in the major until you declare your major. And you cannot declare your major until near the end of Sophomore year (2nd year).

At the time you declare your major, you should already have at least 3 semesters worth of classes and grades. For those first 3-4 semesters, your GPA needs to be 3.0 to get into the engineering program. Junior year is when you actually start taking the main engineering classes.

2.0GPA is usually the GPA required to graduate. Once you get into the major, you no longer need to maintain a 3.0. The 3.0 was just to get in. 2.0 GPA minimum is usually needed to graduate.

What happens if you don't have >=3.0 when you declare your major?
Well each school has a limit on seats. In my college, each engineering major had a limit of 350 new students per year. Lets say only 320 students earned a 3.0 or better for your specific engineering major of interest. That means there are 30 seats open. In that scenario, they will take the next highest GPA (2.99) and accept those students. And so on.

It depends on the school and the department policy. Some departments will tell you that you have x amount of time to get your grades up to par to continue the program. Some will just tell you that you're not meant to be in that program and to switch your major.

They give you an option of either being fed to a vat of maggots or majoring in postmodern French literature. 62% of students choose #1.