Not all states require a special inspection prior to putting a vehicle back on the road, some allow just the basic state safety and/or emissions to suffice.
As far as qualifying for reconstruction thats normally up to the purchaser, how much work and money are you willing to devote to get the vehicle back on the road in accordance with local requirements.
A good place to start discovering why a vehicle was reclassified is the vehicle condition, then asking the seller (not all sellers will be honest so take the answer with a grain of salt). Then study the title, if an insurance company had ownership they normally have no problem divulging why they had it classified. Call them and ask if they have any info on the vin you just purchased that they previously held title to.
Car Fax services can also be helpful.
I normally ask the licensing (DMV) department if they have any title notes, normally someone placed notes on the title record as to why the vehicle was classified, this usually turns out to be my best resource