Can Moonlight Affliction cause a card to have negative Might? What happens if I attempt to give that unit Might afterwards?

Yes, Moonlight Affliction can cause a unit to have negative Might.

How it works:

When Moonlight Affliction resolves, it applies a modifier of -10 Might to the target. If the unit's current Might is less than 10, the result of the calculation will be a negative number. For example, a unit with 3 Might would have -7 Might after the spell resolves.

What happens if you give that unit Might afterwards?

If you later apply a positive Might buff to that unit, the new modifier is added to the unit's current (negative) Might value.

1. Calculation: The game tracks the negative Might value for all calculations. If your unit is at -7 Might and you give it a +3 Might buff, the unit's Might becomes -4.
2. "Treated as 0": While the unit's internal Might value for calculations remains negative, per Rule 143.2.b and associated FAQs (e.g., FAQ #9535), whenever the game checks the unit's Might for interactive purposes—such as dealing combat damage or checking if it is lethal—the value is treated as 0 if it is negative.
3. Lethality: Because the unit is still effectively at 0 or negative Might, it remains highly vulnerable; it will die if it has any non-zero amount of damage marked on it.

In summary: You must first "make up" for the negative Might before the unit's Might will rise above 0. Using our previous example, if you have a unit at -7 Might, you would need to provide a total of +8 Might in buffs to bring the unit up to 1 Might.

Note: This is my interpretation based on the rules regarding Might calculations (Rule 143.2.b) and the standard layering of Might modifiers. No official FAQ exists for this specific interaction with Moonlight Affliction, but it follows the same mechanics established for other Might-reducing effects.