There is NCAA eligibility and there is Ivy League eligibility. The former allows a student to attend classes but compete unattached, thereby maintaining eligibility for that scholastic year (aka "redshirting"). Ivy League eligibility is only a matter of being enrolled: if you are enrolled, you are using your eligibility regardless of your competition status. That, along with the Ivy League prohibition on graduate students competing is why you see Ivy League transfers competing as graduate students elsewhere (e.g., Patrick Brucki having graduated from Princeton, but using his final year of NCAA eligibility at Michigan). So, Ben Darmstadt who beat Brucki both times they competed, only got two years of wrestling due to staying enrolled, injuries, and then graduating. Some things are more important than wrestling in college.
If you want to know a bit more with examples, last year I asked Rob Koll about eligibility of then-current wrestlers (
https://bigredbears.com/forums/viewtopic.php?f=14&t=77) and recruits (
https://bigredbears.com/forums/viewtopic.php?f=14&t=78) including Sokol