Until the official fix comes, here's how you can continue your game and get over the fatal quests bug.

Credits:

Chris K with coming with the idea of locating and editing savegame files to circumvent the fatal bug.

Step 1. Locate your savegame folder

C:\Users\YOUR_WIN_USERNAME\AppData\LocalNow\Full Control\Jagged Alliance Flashback

NOTE: You might need to enable "Show hidden/system files" in Windows. Go to Control Panel --> Folder options:

Step 2. Open World.json in Notepad or Notepad++

In World.json locate TileLocation and change it to a nearby sector you came from.

"Squads": {
    "5": {
      "SquadID": 5,
      "Mercenaries": [
        "CIA_Agent",
        "Louisa_Garneau",
        "Victoria_Waters",
        "Frank_Hennessy",
        "Ice_Williams",
        "Rudy_Roberts"
      ],
      "TileLocation": "C13"
    }

Step 3. Don't do as I did

I landed in a non-existant C12 sector ROFL. Of course, all I had to do was go and edit World.json again.

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To be tested:

Editing quests status in Quests.json to reset them

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Seems like the game doesn't save after you give back the necklace, so you have to manually update the quest.
Looks like you have to edit the following things to finish the farmer's daughter quest:

Quests.json:
QuestStates:
  Q_FarmersDaughter: Completed
GoalStates:
  Q_FarmersDaughter##G2: Completed

World.json:
"Money": (whatever you had there)+1000 (to get the quest reward)
B13:
activeQuest: false (otherwise you still have the quest marker there, this leads to being attacked there again when talking to the farmer)

Editing the current sector is not necessary, as long as you don't talk to the farmer again. You have to restart the game for the changes anyway and after that, your mercs can move freely again.

+1 Chris. 

I've encountered a fatal error where combat won't load when engaging in battle in the bear pit sector (F9). I'm trying to edit my save file so my squad is in a different sector but my save slots only have the files GameLogic.json, World Bin file and the slot setup information. No .json files for memory, quests or world. Any idea how to edit the file without these files? I tried looking in the BIN file but none of the code matched the above discussion. I'd appreciate any help. Thanks in advance.