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Retitle things
Darius Jahandarie
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This usage of いる is unrelated to its usual functions as a grammar element.

〜ている: progressive marker & habitual marker

食事を食べている
"I am eating my meal"
"I eat meals"

〜ていない: negative progressive marker & negative habitual marker

食事を食べていない
"I am not eating my meal"
"I do not eat meals"

〜なくている: normal V1て+V2 compounding

食事を食べなくている
"I do not eat my meal and I exist"

No one would ever say this.

〜ないでいる: adverbial form & means marker

食事を食べないでいる
"I am here (/I exist) without eating my meal." (adverbial)
"I am here (/I exist) by not eating my meal." (means)

In the case of your sentence, context suggests that it is compounding, not a means interpretation; another way to write this form is できずにいる.

Darius Jahandarie
  • 16.5k
  • 4
  • 49
  • 114