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This usage of いる is unrelated to its usual function as a grammar element.

〜ている

食事を食べている
"I am eating my meal" (progressive)
"I eat meals" (habitual)
?? "I eat my meal and I am here (/I exist)" (conjunction)

Reading #3 is never used because no one would ever need to say that. I included it only to show that the て-form does normally perform a conjunction function, it's just very marginal here.

〜ていない

食事を食べていない
"I am not eating my meal" (progressive)
"I do not eat meals" (habitual)
?? "I eat my meal and I am here (/I exist)" (conjunction)

Again, reading #3 is a terrible way to read this sentence and is essentially wrong.

〜なくている

食事を食べなくている
?? "I do not eat my meal and I am here (/I exist)" (conjunction)

This form is never used because there's never a need to say this.

〜ないでいる

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

Reading #1 is Lit. "I am here, in the state of not eating my meal." (It's reminiscent of the stative function 〜ている often performs, but it's slightly different — here, いる is actually still a full-fledged verb and you can't drop the "exist" meaning.)

In the case of your sentence, context suggests that it's a state adjunct, not an instrumental adjunct; another way to write this form is できずにいる.

This usage of いる is unrelated to its usual function as a grammar element.

〜ている

食事を食べている
"I am eating my meal" (progressive)
"I eat meals" (habitual)
?? "I eat my meal and I am here (/I exist)" (conjunction)

Reading #3 is never used because no one would ever need to say that. I included it only to show that the て-form does normally perform a conjunction function, it's just very marginal here.

〜ていない

食事を食べていない
"I am not eating my meal" (progressive)
"I do not eat meals" (habitual)
?? "I eat my meal and I am not here (/I don't exist)" (conjunction)

Again, reading #3 is a terrible way to read this sentence and is essentially wrong.

〜なくている

食事を食べなくている
?? "I do not eat my meal and I am here (/I exist)" (conjunction)

This form is never used because there's never a need to say this.

〜ないでいる

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

Reading #1 is Lit. "I am here, in the state of not eating my meal." (It's reminiscent of the stative function 〜ている often performs, but it's slightly different — here, いる is actually still a full-fledged verb and you can't drop the "exist" meaning.)

In the case of your sentence, context suggests that it's a state adjunct, not an instrumental adjunct; another way to write this form is できずにいる.

This usage of いる is unrelated to its usual functions as a grammar element.

〜ている

食事を食べている
"I am eating my meal" (progressive)
"I eat meals" (habitual)
?? "I eat my meal and I am here (/I exist)" (conjunction)

The 3rd reading is absolutely never used because of how useless it is semantically -- I included it because it's relevant to see a pattern.

〜ていない

食事を食べていない
"I am not eating my meal" (progressive)
"I do not eat meals" (habitual)
?? "I eat my meal and I am here (/I exist)" (conjunction)

Again, the 3rd reading is a terrible way to read this sentence and is essentially wrong.

〜なくている

食事を食べなくている
?? "I do not eat my meal and I am here (/I exist)" (conjunction)

This form is never ever used because there is no reason to ever use this meaning.

〜ないでいる

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

The state adjunct reading has semantics like "I am here, in the state of not eating my meal." You may consider this similar to the stative function 〜ている often performs, but it is slightly different -- here, いる is actually still a full-fledged verb and you can't drop the "exist" meaning.

In the case of your sentence, context suggests that it is a state adjunct, not an instrumental adjunct; another way to write this form is できずにいる.

This usage of いる is unrelated to its usual function as a grammar element.

〜ている

食事を食べている
"I am eating my meal" (progressive)
"I eat meals" (habitual)
?? "I eat my meal and I am here (/I exist)" (conjunction)

Reading #3 is never used because no one would ever need to say that. I included it only to show that the て-form does normally perform a conjunction function, it's just very marginal here.

〜ていない

食事を食べていない
"I am not eating my meal" (progressive)
"I do not eat meals" (habitual)
?? "I eat my meal and I am here (/I exist)" (conjunction)

Again, reading #3 is a terrible way to read this sentence and is essentially wrong.

〜なくている

食事を食べなくている
?? "I do not eat my meal and I am here (/I exist)" (conjunction)

This form is never used because there's never a need to say this.

〜ないでいる

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

Reading #1 is Lit. "I am here, in the state of not eating my meal." (It's reminiscent of the stative function 〜ている often performs, but it's slightly different — here, いる is actually still a full-fledged verb and you can't drop the "exist" meaning.)

In the case of your sentence, context suggests that it's a state adjunct, not an instrumental adjunct; another way to write this form is できずにいる.

This usage of いる is unrelated to its usual functions as a grammar element.

〜ている

食事を食べている
"I am eating my meal" (progressive)
"I eat meals" (habitual)
?? "I eat my meal and I am here (/I exist)" (conjunction)

The 3rd reading is absolutely never used because of how useless it is semantically -- I included it because it's relevant to see a pattern.

〜ていない

食事を食べていない
"I am not eating my meal" (progressive)
"I do not eat meals" (habitual)
?? "I eat my meal and I am here (/I exist)" (conjunction)

Again, the 3rd reading is a terrible way to read this sentence and is essentially wrong.

〜なくている

食事を食べなくている
?? "I do not eat my meal and I am here (/I exist)" (conjunction)

This form is never ever used because there is no reason to ever use this meaning.

〜ないでいる

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)

The adverbial reading is similar to conjunction, but critically its semantics are something like "I am here in the state of not eating my meal." (If someone can think of a good name for this form aside from just 'adverbial' I'd love to hear it.)

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

This usage of いる is unrelated to its usual functions as a grammar element.

〜ている

食事を食べている
"I am eating my meal" (progressive)
"I eat meals" (habitual)
?? "I eat my meal and I am here (/I exist)" (conjunction)

The 3rd reading is absolutely never used because of how useless it is semantically -- I included it because it's relevant to see a pattern.

〜ていない

食事を食べていない
"I am not eating my meal" (progressive)
"I do not eat meals" (habitual)
?? "I eat my meal and I am here (/I exist)" (conjunction)

Again, the 3rd reading is a terrible way to read this sentence and is essentially wrong.

〜なくている

食事を食べなくている
?? "I do not eat my meal and I am here (/I exist)" (conjunction)

This form is never ever used because there is no reason to ever use this meaning.

〜ないでいる

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

The state adjunct reading has semantics like "I am here, in the state of not eating my meal." You may consider this similar to the stative function 〜ている often performs, but it is slightly different -- here, いる is actually still a full-fledged verb and you can't drop the "exist" meaning.

In the case of your sentence, context suggests that it is a state adjunct, not an instrumental adjunct; another way to write this form is できずにいる.