放って is 放る. We say ほうる・ほうって. Your OP sounds 3: "to leave somebody/something alone".
And くる in your OP is called 補助動詞 くる. Perhaps it's 17-イ, and means that you (go) leave somebody/something alone and will come back.
あんな状態のまま doesn't sound that this 状態 is a good one.
If you're going to leave somebody alone, it'd be "I leave him or her alone in such a (bad) status and will come back."
Or that can mean that you sustain/keep the bad status (When you don't have somebody to set in that status).