For me, how I'd handle it would vary from collection to collection. For video games, I'd rebuild, but it'd be more selective, mainly just reacquiring the games from my childhood for nostalgia's sake. With the newer systems, I'd probably stop buying physical almost altogether and just stick with digital, especially with how Microsoft and Steam are handling things as I just punch in my account into a new machine and I'm back up and running. Hell, my Steam inventory is worth more than my entire physical collection at this point.
As for my other collections, I likely wouldn't rebuild my trading card and vintage action figure collections, mainly as I never get a chance to play the card games anymore and that the figures I collect have been getting harder to find decent deals on. My book and Lego collections I'd certainly rebuild, but with more new stuff than trying to reacquire what I'd lost. And I'd rebuild my board game collection, but a bit more discerningly, so I'd only be grabbing games with staying power in my game group rather than ones we've only played once and called it good.