It all depends on the TOTAL text in the contract. Does it say anything about allowing 'adjustments' due to errors?? Does it say anything about amendments, etc???
Call the fence company and ask them to tell you where in THEIR contract does it allow for them to adjust the price, and where it allows them to void the contract for their error.
If they can't show you BOTH of these provisions, then tell them that you expect to look out and see your new fence in accordance with the contract, or that you will have to have your fence installed by another contractor and sue them for your damages (the difference between their price and what you actually pay.... plus your 50% 'deposit', plus costs, plus attorney, plus interest!!!).
Then, if they don't 'realize their error' and complete their contract, you will need to start making your case. Send them a confirming letter (certified RRR) detailing the above demands. Give them 10 (?) days to respond. If they don't, move forward.