Your confusion is understandable. The section on active physical skills (page 133 of the Core Rulebook) does not go in-depth into discussing how fall damage works in combination with the Free-Fall skill. The next page (134), however, under the section on Climbing Failures and Glitches refers you to page 172 for Falling Damage.

Falling Damage

When a character falls more than three meters, he takes Physical damage with a DV equal to the number of meters fallen, with an AP of –4. Use Body + Armor to resist this damage. The gamemaster should feel free to modify the damage to reflect a softer landing surface (sand), branches to break the fall, and so on. Falling characters drop 50 meters in the first Combat Turn, 150 meters in the second Combat Turn, and 200 meters every Combat Turn after that. Terminal velocity for a falling body is about 200 meters per turn.

Again, no guidance is given in using the Free-Fall skill. So the GM needs to apply their own discretion. Here's how I do it assuming that the character doesn't have any gear designed to help them overcome falls such as grappling hooks, parachutes, etcetera.

1. Since Body is the linked attribute for Free-Fall, the dice pool for the Free-Fall test is Body + Free-Fall. Note that Free-Fall allows characters to default (see page 130) if they don't have any ranks in the skill, using Body - 1 as the dice pool for the test. Since the pool is derived from an attribute and a skill, a limit applies. Seeing as it's a physical skill, it makes sense to use the character's physical limit.
2. If the distance the character is falling is 50 meters or less, the test is a simple success test. If the distance is greater than 50 meters, the test is an extended test with an interval equal to the number of combat turns that it will take for the character to hit the ground.
3. If it's a simple test, the threshold is two successes. Once that has been met, each additional success acts as the Light Body adept power or Rolling Cloud martial art technique reducing the effective distance of the fall by one meter when calculating the character's falling damage. This effect stacks with Light Body and Rolling Cloud.
4. If it's an extended test, the threshold is equal to the number of combat turns that it will take for the character to hit the ground squared (4 successes for 2 combat turns, 9 successes for 3 combat turns, 16 successes for 4 combat turns, etcetera). Once that has been met, each additional success reduces the effective distance of the fall by five meters when calculating the character's falling damage. This effect stacks with Light Body and Rolling Cloud.

The "Break-Fall" Free-Fall specialization is applicable to this test, granting a +2 dice pool bonus to characters attempting to break a fall.

The reason that I increase the threshold quadratically is to represent the fact that the greater the fall distance (and thus more time spent falling), the more speed gets built up and the harder it is to successfully break the fall.

If we assume that all spells and items at your disposal restore your health by regaining hit points, and we also assume that all the damage dealt to our hypothetical character was dealt by the Sword of Wounding, it would seem that the character is eternally stuck at 0 HP.

However, let us turn to the "Recuperating" downtime activity listed on page 187 of the PHB (emphasis mine):

You can use downtime between adventures to recover from debilitating injury, disease, or poison.

After three days of downtime spent recuperating, you can make a DC 15 Constitution saving throw. On a successful save, you can choose one of the following results:

• End one effect on you that prevents you from regaining hit points.
• For the next 24 hours, gain advantage on saving throws against one disease or poison currently affecting you.

So, after 3 days you can make a DC 15 Con save to try and remove the effect of the Sword of Wounding from your character. If you fail, you can try again in another 3 days, provided that your unconscious body is actually allowed to have downtime to recuperate (i.e. left to rest somewhere in a bed, while the rest of the party does their own downtime activities). Once you have made the save, you are both:

• stable at 0 HP, and
• able to regain hit points again, meaning that in 1d4 hours you will be back up with 1 hit point (or sooner with potentially more HP if you receive healing).