CLT may fail under this condition? CLT says that when sample size n goes to infinity, the sample sum or average curve converges to normal distribution.
My question is: if the sample size goes closer or even equal to the population size, wouldn't the average values cram so closely near the mean, that violate the "bell shape" distribution?

Random variables are generally modelled as coming from an infinite population. Even when we're sampling from a finite set of instances, we can still view the population as being infinite. For instance, if you have an urn with 10 red balls and 30 green balls, you can consider your random variable to be "the color of a randomly selected ball", and as long as you do your selection with replacement, you can select balls an infinite number of times. Furthermore, you can model the situation as there being some process that created each of the balls in the urn, and you can imagine what you would get if you were to get an infinite number of balls from whatever process that is.
If you do treat your population size as being finite, and you sample without replacement, then the conditions of CLT are not satisfied. The classical formulation of the CLT requires that the random variables be from identical distributions with a finite variance, and each random variable be independent of each other. The first two conditions can be relaxed for a more general statement, but having the random variables be dependent on each other can reduce or even eliminated the convergence to a gaussian distribution. If you draw from a finite population without replacement, then each draw affects the remaining population, and thus further draws are dependent on earlier ones, violating the conditions of the CLT.
