What Happens if a Title Defect is Discovered?

That depends on which Purchase Contract is being used for the transaction.

For the Florida REALTORS Contract For Sale and Purchase (CRSP):

10 (b) Title Examination: Buyer will examine the title evidence and deliver written notice to Seller, within 5 days after receipt of title evidence but no later than Closing Date, of any defects that make the title unmarketable.
Seller will have 30 days after receiving Buyer’s notice of defects ("Curative Period") to cure the defects at Seller’s expense. If Seller cures the defects within the Curative Period, Seller will deliver written notice to Buyer and the Closing will occur on Closing Date or within 10 days after Buyer receives Seller’s notice if Closing Date has passed. If Seller is unable to cure the defects within the Curative Period, Seller will deliver written notice to Buyer and Buyer will, within 10 days after receiving Seller’s notice, either cancel this Contract, extend Curative Period for a specified period not to exceed 120 days, or accept title with existing defects and close the transaction.

For the FAR-BAR "AS-IS":
18 (ii) TITLE EXAMINATION: Buyer shall have 5 days after receipt of Title Commitment to examine it and notify Seller in writing specifying defect(s), if any, that render title unmarketable. If Seller provides Title Commitment and it is delivered to Buyer less than 5 days prior to Closing Date, Buyer may extend Closing for up to 5 days after date of receipt to examine same in accordance with this STANDARD A. Seller shall have 30 days (“Cure Period”) after receipt of Buyer’s notice to take reasonable diligent efforts to remove defects. If Buyer fails to so notify Seller, Buyer shall be deemed to have accepted title as it then is. If Seller cures defects within Cure Period, Seller will deliver written notice to Buyer (with proof of cure acceptable to Buyer and Buyer’s attorney) and the parties will close this Contract on Closing Date (or if Closing Date has passed, within 10 days after Buyer’s receipt of Seller’s notice). If Seller is unable to cure defects within Cure Period, then Buyer may, within 5 days after expiration of Cure Period, deliver written notice to Seller: (a) extending Cure Period for a specified period not to exceed 120 days within which Seller shall continue to use reasonable diligent effort to remove or cure the defects (“Extended Cure Period”); or (b) electing to accept title with existing defects and close this Contract on Closing Date (or if Closing Date has passed, within the earlier of 10 days after end of Extended Cure Period or Buyer’s receipt of Seller’s notice), or (c) electing to terminate this Contract and receive a refund of the Deposit, thereby releasing Buyer and Seller from all further obligations under this Contract. If after reasonable diligent effort, Seller is unable to timely cure defects, and Buyer does not waive the defects, this Contract shall terminate, and Buyer shall receive a refund of the Deposit, thereby releasing Buyer and Seller from all further obligations under this Contract.