Offer accepted, now what? What if seller decide to accept higher bids?

Today my offer was accepted, i was the only offer as i sent it just 5 days the listing went public. Now im talking to the lawyer for the due diligence and prepare the contract, but i heard it can still happen that someone can arrive tomorrow and outbid me. who's going to pay lawyer's fee? is it even fair?

​

UPDATE:

the seller finally signed the contract. Ernest money sent. my lawyer has been very diligent, maybe too much, and made me very nervous to wait almost 10 days to enter the contract. what a relief.