If I eclipse a unit to 0 or negative health at a battlefield does it die?

No, using Eclipse to reduce a unit's Might to 0 (or lower) does not automatically kill it.

According to RiftJudge FAQ #9491 and Rule 143.2.a, a unit is only killed if it has non-zero damage marked on it equalling or exceeding its Might. Reducing a unit's Might does not count as dealing damage.

Here is how the interaction works:

• If the unit has no damage on it: Even if its Might is reduced to 0, it will remain on the battlefield alive.
• If the unit already has damage on it: It will only die if that damage is non-zero and equal to or greater than its new, reduced Might value.

Additionally, per Rule 143.2.b, a unit with 0 or less Might is treated as having 0 Might for all interactive purposes, but it still does not die simply by reaching that state.