Helmeppo [OP03-091]

I activated this [On Play] effect against my opponent's Character with a base cost of 6 when I had [OP02-121 Kuzan] on my field and the "[Your Turn] Give all of your opponent's Characters −5 cost." effect was active. If [OP02-121 Kuzan] then leaves the field on that turn, does this Character's cost become 0?

In this case, the cost becomes 0.