On chain A blocks bigger then 1mb will be valid
On chain B blocks bigger then 1mb will be invalid
Now when you sign a transaction and broadcast it, it will get executed on both chains.Unless the transaction has coins in one of its inputs that already went through a block bigger then 1mb. Then the transaction is only valid in chain A. This way you can double the value of a coins that are spendable on both chains. Because now you can sell them once on chain A and once on chain B.
Anyway, I think this is extremely unlikely to happen, because:
1) It requires 50% of miners to cooperate to even create a >1MB chain
2) Anyone using the old chain would be insecure, due to lack of mining power making it susceptible to a 51% attack.
3) If that many miners were on board, it's unlikely that existing core developers would opt to continue working on an insure fork rather than admit defeat.
4) If that many miners were on board, it's unlikely that exchanges would opt to confuse users by letting them separately trade two different types of Bitcoin, rather than just switching to the more secure, more popular chain.