You have 1 satoshi in address 123 which represents a share, or ounce of gold, or $1 USD, etc. I make a transaction transferring 100 satoshis to address 123.
I was going to say that you destroy your satoshi by doing so, "donating" the amount to the issuer.
I just now realized you cannot prevent some jackass to go on destroying everybody backed coins, if that's so.
Good point, I hadn't thought it before.
Let's think... the address containing the tainted coins is now "polluted" with other, non-backed coins. While everything remains there, one can still guess how much backed coins are there, and how much normal ones. This address in under control of someone who's interested in not losing track of the backed coins.
We could assume as rule that the first transaction with the correct amount (one satoshi in your example) to leave address 123 is the one sending the tainted satoshi. Any subsequent transaction is just normal bitcoin. If you, in control of address 123, spend all coins in it without making a single transaction of the appropriate value (1 satoshi), then you just voluntarily destroyed your own backed coin.
Obviously, a software meant to deal this with this protocol should prevent you from destroying your backed coins.
Answering your last question, if we use the rule above, it should be Person A the new owner, since it was the first.
There's still a potential issue: you send 1 satoshi to two different address in two different transactions with the exact same timestamp, and both get confirmed on the same block. We can't know which is the first in this case. We could treat such case as identical to a single transaction with 2 satoshis being sent to different outputs, thus, not a "backed coin transaction" since it's not the correct amount. Again, software should prevent you from doing this accidentally.
This "following tainted coins" code/protocol could be useful in many different use cases, I think. A satoshi may reference pretty much anything, and be used in contracts. Like that smart property proposition. There are probably even more use cases for it that I just can't think of.