I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear that this happened.
Unless the contract says "Time is if the essence," a homeowner
unfortunately does not have a right to cancel a contract and refuse payment just because the work is not completed on time. You're required to give him a reasonable time to finish the job. Otherwise, you're in breach of the contract.
A contract is allowed to place a lien whenever he is owed money for work performed or materials purchased, if it's more than $500. If he places the lien, he can either leave it there until you want to sell the property, at which point you'd have to pay him, or he could sue to foreclose the lien, which would mean the property could be sold out from under you - even if you aren't past due on your mortgage
If the judge finds in your favor, he would be required to remove the lien or he's in contempt of court and he could be sued for damages
One way to avoid a problem with the property being tied up is to pay the contractor, write "under protest" on the check, and then sue for a refund. But the judge could find in the contractor's favor if you didn't give him a chance to finish the job (even if he missed the deadline).
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