I feel like with rats it’s never possible to completely eliminate them, only manage the population numbers. I had some living under the garage and set a cage traps which has been very successful. My tally is 15. I have no resident rats anymore but I do still catch the occasional visitor/scout...
Sounds like yes the chick got out early and got lost or taken by predators, or a rat came in and took it.
If it was rats, they will be able to chew through any kind of fabric. Use steel wool instead, apparently they don’t like that.