If a unit has 1 HP left because a spell inflicted me damage and my opponent gives me -4 might to that unit, does the unit die?

Yes, your unit will die.

In Riftbound, there is no "HP" stat; units have a Might value, and damage is tracked separately as marked damage. A unit is killed when it has non-zero damage marked on it that is equal to or greater than its current Might.

According to Rule 143.2.a and multiple FAQs (such as FAQ 8256):

• Your unit has 1 damage marked on it.
• Your opponent reduces its Might by 4.
• Even if the unit's Might was originally high, if it is reduced to a value less than or equal to the damage marked on it (in this case, 1 or less), the unit dies during the next cleanup.

Since you mentioned the unit had 1 damage marked on it and received a -4 Might reduction, its current Might is now less than or equal to the damage marked on it, causing it to be killed.