Are you the buyer or the seller?
If the auction is closed and someone contacts you with another, higher bid, too bad for him (and you). It would be unethical (and difficult) to refuse the winning bidder.
To say nothing of dealing with someone who is unwilling to follow the normal, protected procedures.
If you are a bidder and someone bids higher than you, bid again.
The usual advice is : bid once, bid your maximum.
The eBay 'bots won't push your bid any higher than you have instructed them. That can be trusted.