How to account for reduced student capacity when calculating program retention?
Rationale
Some of the terms are a little vague, particularly what you refer to as eligible students and returned students. I'll set some variables for clarity, but tell me if I defined them incorrectly.
I assume them to mean:

eligible students $ = A $ being the set of all students in the after-school program 2019-2020

returning students $ = A\cap S $ where $S$ is the set of all of summer camp 2020 students
Now we can define retention rate to be $\frac{|A\cap S|}{|A|}$. I base this on the US government definition of university student retention rate, which I think is pretty similar, but please correct me if it's not.

The reasons as to why you might have $|A\cap S|&lt;|A|$ are irrelevant.

Example
Let's say you have $|A|=100$ so that, in your situation, $|S|=90$. For simplicity, let's also say that there are no newcomers to the mix.
The retention is, quite literally, how many students you retained. If you retained $90$ students, then the retention rate is $90/100$. Even though $|S|=|A|-10$, the number of students you retained $|A\cap S|$ as a percentage of the number of students in the original program $|A|$ is still $90\%$.
It wouldn't make sense to normalize this to $100\%$.