A person can serve as President a total of 10 years. That is to say, a person can serve as President the last 2 years of someone else's term and then go on to serve 8 more years. Now, I don't know how this plays into the next provision.
Quick and dirty scenario.
Biden runs for President with Obama as his VP running mate. They win.
For whatever reason, Biden cannot serve out his full term in office. He gets sick, he dies, or...he resigns. Obama could legally step in as President again.
I'm NOT saying this is probable. I'm saying it's legally possible.
And that's why I said, if anyone bothers to read my post, "under the right conditions" he can come back. And note that I said, "one can dream". In other words, it's possible though not probable.
Would they do it? Probably not.
Could they? Yes, they could.
Again, I'm not at all sure that the 10 year rule applies to the above. I don't think that it is clearly stated that it does.
ETA: If the 10 year rule does apply, I think he could serve the last 2 years of Biden's term as President.