Short Answer
Bona fide purchaser without notice status (often abbreviated BFP) is usually evaluated at the time that the BFP takes title. Subsequent knowledge of defects in the title of the seller who sold to the BFP doesn't impair the ability of the BFP to convey good title to someone else.
Long Answer
I'll analyze the real estate and motor vehicle cases separately because title works differently for real estate than it does for motor vehicles even though both apply similar concepts.
Real Estate
Hence, in the case of real estate, when the BFP receives delivery of an executed deed and records it (there is a bit of trickiness in the very brief time period between the receipt of delivery and recording).
For example, suppose that Joe, a BFP buys real estate from Fred, a con man who acquired title from Sally at far less than market value through fraud in the inducement by telling her that it wasn't zoned for marijuana growing when it actually was zoned for that. A week after Joe closes on the sale from Fred (in which the deed to Joe from Fred was recorded in the real property records the same day), Joe learns that Sally was defrauded by Fred. After this happens, Joe can still convey good title to that real estate to Martin, even if both Joe and Martin know that Sally was defrauded by Fred and that Joe's title is rooted in the sale to Fred.
But, on the other hand, if the buyer had notice of the defect in the seller's title after entering into a contract to purchase the real property, but before receiving delivery of and recording a deed to the real property purchased, this person would not be entitled to BFP status, and the buyer's title would also be voidable.
The time that the buyer acquired physical possession of the real property, for example by receiving the keys or entering onto the property (which is related to the archaic concept of "livery of seisin", that typically involved the symbolic delivery of a twig or cupful of dirt from the property purchased in pre-modern times) wouldn't matter.
Motor Vehicles
In the case of a motor vehicle, BFP status is evaluated when the BFP receives delivery of the executed certificate of title transferring title to the BFP.
For example, suppose that Joe, a BFP, buys a Buick from Fred, and has received a certificate of title signed by Fred whom the certificate of title which is a genuine certificate of title issued by the state, has signed. Fred got his title to the Buick from Sally who sold it to him in exchange for a bag of beans that Fred told Sally were magic beans but were actually just ordinary beans from the grocery store. Fred had voidable title to the Buick. But Joe can convey good title to the Buick to Martin, even if after receiving the certificate of title from Fred, both Joe and Martin become away that Sally was defrauded by Fred.
But the buyer would not attain BFP status if the buyer obtained title after a contract of sale was signed but before the certificate of title was executed and delivered to the buyer.
The time that the buyer obtained physical possession of the car wouldn't matter.
Subsequent knowledge of irregularities in the title of the person who transferred the real estate or motor vehicle to the BFP after these events shouldn't impair the ability of the BFP to convey good title.
What Is Necessary To Overcome BFP Status And Are There Exceptions To The Void Title Exception To BFP Status?
As noted in the answers to the question referenced in this question, one can't be a BFP if your chain of title in rooted in a thief. But, this consideration is mitigated quite a bit in both real estate and motor vehicle contexts due to the laws regulating transfers of title in those cases. It takes pretty extreme facts for their to be a void title to real estate or a motor vehicle.
Also, even void title could provide a basis for a much slower to accrue claim of adverse possession to real estate or a motor vehicle by a BFP whose protections don't apply because the root of the title is in a thief. There are fact patterns where title by adverse possession is a plausible possibility the case of a BFP of real estate with a void title. But it is almost impossible for a BFP with void title to acquire ownership of a motor vehicle through adverse possession.
What Does A Void Root Of Title In Real Estate
In the real property case, where the BFP has received a deed, one would have to show basically that the root of the BFPs title was a forged or counterfeit deed, or a "wild deed" (i.e. a deed from one person to another by someone who had no color of title to the property of any kind of that time of the execution of the deed and also didn't have after acquired title).
Adverse Possession Of Real Estate Rooted In A Void Deed
The first person to receive a deed in the BFPs chain of title, however, would start the clock running on the adverse possession period
Colorado with an 18 year adverse possession period (for the claimant's entire chain of title), in general, and a 7 year and color of title adverse possession period (for the claimant's entire chair of title) where the person seeking to claim adverse possession received a deed as a BFP, even if it was a void deed, would be pretty typical time periods with some longer and some shorter.
So, even if BFP doctrines fail in real estate, adverse possession laws could have a similar effect to the BFP doctrine in a real estate case.
What Does A Void Conveyance Of A Motor Vehicle Look Like?
In the motor vehicle case, the certificate of title would have to be counterfeit, to overcome BFP status. Anyone with a state issued certificate of title saying that they own the motor vehicle can transfer good title to the motor vehicle to a BFP.
Also, one would look no further to the root of title that the immediate seller in the case of the motor vehicle, because the state in which the vehicle is titled reissues a new certificate of title each time there is a change of ownership.
Adverse Possession Of A Motor Vehicle With A Void Title
Adverse possession could potentially be implicated even if BFP protections fail in the motor vehicle case as well, particular if the BFP of the vehicle that the seller didn't own was registered with the state.
But adverse possession in the case of a motor vehicle would take an extremely unusual fact pattern, because normally a BFP's title won't be registered by the state without review of the certificate of title and a certification of VIN number. Usually, the BFP receiving a counterfeit certificate of title would learn of the fraud right away in the process of trying to get the car registered and trying to get new license plates for the car.
Also, possession of the car and a signed and delivered certificate of title without registering the car with the state (by filing the certificate of title received), and without trying to get new license plates, would probably not satisfy the "open and notorious" possession requirement of a claim that the buyer owns the car by virtue of adverse possession.