if I play a spell that reduces the height of a unit that unit go to negative might

Yes — a unit's Might can be reduced below 0 (e.g. a 2[M] unit hit with -4 becomes -2[M]), so there's nothing stopping the reduction from going negative (CR 143.2.c).

The important part is how that negative number is treated afterwards. For calculating further increases/decreases the game keeps the real value — a -3[M] unit given +2[M] becomes -1[M], not +2[M]. But whenever the game checks the unit's Might (combat damage it deals, lethal damage, "Might 4 or greater" style requirements), a negative value is read as 0 (Rule 710). A unit at 0 or less Might doesn't die just from the reduction; it dies if it has damage marked on it equal to or greater than its current Might — and at 0 Might, even 1 damage is lethal.

One nuance: if the reduction is capped ("-4[M] to a minimum of 1"), that cap is snapshotted at the moment it applies (Rule 479.4.b), so later Might changes don't undo it.