If you're engaging in a PPT, you are transferring the gun. You can buy and sell things with a verbal contract and an exchange of money and goods, what you are doing here is the legal process for you to take possession of the gun.

Here is what I like to do if I don't know the other party I am buying from - Meet them in the store, talk to the FFL employee, and inspect the firearm. If I like it, leave the firearm with the FFL assuming they are cool with it, and go outside to my car, where I have two copies a simple bill of sale written up. It says 'I sold this gun with serial number # on this date to this person". We sign both and each get a copy. Then I pay them, we go back inside and complete the FFL paperwork for the transfer. After that I never have to see them again and just come back after the 10-day.

What happens if we do the PPT and the gun is stolen or has something else that comes out during the DROS?

In this highly unlikely event: The gun will probably get seized by law enforcement and you will either have to arrange with the seller to get your money back, or not, or take them to court if you believe they knowingly sold you stolen merch and attempt to get a judgement in your favor. If it's a problem on your end that comes back well after the transfer paperwork was submitted, you still own the gun but you can't take possession of it. What the FFL, as custodian of the firearm, does in this situation will influence your options. The seller has no legal obligation to return or re-take possession of a weapon once it's been sold and legally transferred.