In the song "ברוך א׳ עליון" (text) is the line:
וְהוּא יִדְרֹשׁ לְצִיּוֹן עִיר הַנִּדָּחָה
My grandfather, ע״ה, when singing this line, would replace הַנִּדָּחָה with another word (I think הַנִּשְׁבָּרָה). The reason for this is that there's a concept in קדשים of "כיון שנדחה ידחה" (once something is נדחה, 'pushed away' from being allowed on the altar, it's forever נדחה and can never be allowed on the altar). Saying Tziyon is forever 'pushed away' is both false and seemingly in denial of the coming of the third bes hamikdash, and my grandfather, apparently, or whomever he got this practice from, didn't want to even seem to imply it.
My question is whether this is a documented or known practice or version. (Not necessarily replacing הנדחה with הנשברה specifically, but with anything.) Where could my grandfather have gotten it from? A second question is whether anyone comments on the inappropriateness of the line in light of "כיון שנדחה ידחה".