The title doesn't explain my question very well, so I will use an example to explain this further.
Say, I record the percentage of people exiting a supermarket from $1-2\text{pm}$ who use their own bag instead of a plastic bag for $100$ days. Say, that the data I obtain is approximately normal. Can a normal distribution be used to model this despite the fact that $x$ terminates at $0\text{% and } 100\text%$ because it's a percentage?
The normal distribution extends to infinity in both directions, but it is very small a few standard deviations from the mean. You can create a new distribution by truncating the normal distribution at some limits. You should rescale the distribution to keep the area $1$, but if you only cut off the tails that is a small effect.