Insurance
Depending on your insurance company, you can get full coverage on the vehicle, BUT, in the event that it becomes involved in another accident that causes another total loss event, the insurance company will probably only pay 50% of the retail value of the vehicle at the time of loss.
For example: if you had an $8K mini van that was a total loss, the insurance company (prior to settlement) runs a title check, discovers it's a prior total, you'd most likely get $4K, less your deductible.
I work in insurance on the claims side & that's how we generally handle that situation. Most people that know they had a prior total are fine with that. The problems start when the poor owner never knew the vehicle was a prior total......