What do you mean by "tanks"?
Every PBN is a money site that monetizes in one way or another and it provides value to targeted visitors that have commercial intent. This way Google has absolutely no reason to deindex it, and you're not only making your main money sites stronger, but make additional buck along the way from your PBNs.
The problem with people that cuss PBNs is that most often they create churn and burn network without realizing it, and the sole use of them is to point to their money sites with spun content that has absolutely no value at all.
Are you looking for a good backlink profile for an expired domain that you find?
A clean inbound link profile is absolutely crucial. That's the first thing I look out for followed by a number of referring domains, IPs and subnets and their ratio to back links.
If an expired domain was spammed before, even just a tad, I move on. I usually don't pay too much attention to any metrics such as DA or PA as these are made up numbers that really don't mean anything. Trust Flow is something I'd consider if a domain doesn't have strong back links, but then it has to have a good ratio against Citation Flow. Most of the time though, if a domain has quality links then TF and TF/CF ratio are intact anyways. There's quite a few things to consider and there's no one simple advice to follow.
Do you use a domain finder service, or do you have a process that you follow?
I mostly use SB, DHG, DomCop and occasionally ExpiredDomains and I run all domains against my own scripts that use Majestic and Ahrefs APIs and I review every single one of them manually before I register any of them.