You said this last year, just before at least FOUR rookies we cut on cutdown day ended up on other teams, maybe more. Clint Oldenburg and Kareem Brown were signed by the Jets, Corey Hilliard by the Colts, and Justin Rogers by the Cowboys. Some teams who have little depth are happy to sign players cut by teams who are deep or teams with a track record of drafting good players.
There were rookies we cut the previous year who ended up on other teams, also. Jeremy Mincey and Garrett Mills come to mind. JAX and MIN had no problem cutting a guy who was familiar with their system in favor of these two who they never had on the practice field.
If you follow signings for the entire NFL closely in the few days after cutdown day, you'll see there are a LOT of signings and cuttings and teams tweak rosters.
I'm not saying any of our guys will or will not pass through waivers. No one can tell that ahead of time. But to say that waiver claims are rarely made after cutdown day is just incorrect.
If you cut a guy, you had best plan on losing him. That is the only way to look at it. If you want to keep him for next year and don't want to lose him, keep him or IR him if that is possible.