What's the いて in 「忘れないでいて」 for?


I know that the verb changes from 忘れる(to forget) to 忘れないで (don´t forget) but I
can´t understand the いて at the end. At first, I thought it comes from the
casual imperative form of いる as [this post
explained](https://japanese.stackexchange.com/questions/34332/whats-the-
grammar-of-%E3%81%A6-form-%E3%81%84%E3%81%A6) but it must have a verb in a
て-form before to have this "keep...ing" meaning or to make the request.

This is from a song called "Name of Love", the lyrics are as follows:

> 未来で逢えるなら 忘れないでいて 僕のこと 本当のこと




You have found the correct question; this いて is a [subsidiary
verb](https://japanese.stackexchange.com/a/18965/5010) that means "to be ～ing"
or "to keep ～ing". What you are missing is that 忘れないで is _basically_ a
(negative) te-form. ないで can be followed by many subsidiary verbs including いる,
おく, やる and くださる. See: [Is ないで a te-
form?](https://japanese.stackexchange.com/q/11473/5010) and [ないで vs なくて:
combining phrases with negative
verbs](https://japanese.stackexchange.com/q/5925/5010)

So 忘れないでいて means "(Please) don't forget me (for some time)" or "Keep
remembering me."




You have found the correct question; this いて is a [subsidiary
verb](https://japanese.stackexchange.com/a/18965/5010) that means "to be ～ing"
or "to keep ～ing". What you are missing is that 忘れないで is _basically_ a
(negative) te-form. ないで can be followed by many subsidiary verbs including いる,
おく, やる and くださる. See: [Is ないで a te-
form?](https://japanese.stackexchange.com/q/11473/5010) and [ないで vs なくて:
combining phrases with negative
verbs](https://japanese.stackexchange.com/q/5925/5010)

So 忘れないでいて means "(Please) don't forget me (for some time)" or "Keep
remembering me."

