[RPG] a monster’s hit dice found in the stat block

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).

If their maximum hit points is zero then healing magic won't do anything. Healing magic allows a character to "regain" or "restore" hit points, which is always up to your maximum.

When a creature receives healing of any kind, hit points regained are added to its current hit points. A creature's hit points can't exceed its hit point maximum, so any hit points regained in excess of this number are lost.

Basic Rules, Combat chapter.

This disallows cure wounds and healing word and their mass versions, prayer of healing, goodberry (assuming you can feed a berry to an unconscious person) and pretty much all healing potions.

One spell that will help is aid - as long as you keep casting it over and over again.

Your spell bolsters your allies with toughness and resolve. Choose up to three creatures within range. Each target's hit point maximum and current hit points increase by 5 for the duration.

Please note that many effects that reduce maximum hit points also specify really bad things for when the character reaches 0 (for example, the strength drain attack of a shadow). Keeping someone conscious isn't much of an issue when they've turned into an undead monster and are trying to eat your face.