Without Fail, Unconditionally
Adverb
ぜったい
学校のある夜は、外出できないって言ってるでしょ。だめだと言ったら絶対にだめだからね！
You can’t go out on a school night. If I say it’s no good, it’s absolutely no good!
Extinction will happen as you go versus extinction. It will happen absolutely. It will happen without fail. There's nothing you can do to stop extinction.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well. Be careful though, 絶 is normally read as ぜつ, but in this case it is shortened to ぜっ.