na-adjective, noun which may take the genitive case particle 'no'
dead drunk; blotto; plastered
Colloquial and emphatic; describes someone who is completely intoxicated, often to the point of being unable to function properly.
昨夜はへべれけになるまで飲んでしまった。
Last night I drank until I was dead drunk.
彼はへべれけでまっすぐ歩けなかった。
He was so plastered he couldn't walk straight.
The origin is uncertain; it is a colloquial mimetic-like expression for extreme drunkenness, possibly derived from the sound or feeling of being helplessly drunk.