Strange use of volitional form?

[Chabichou]

I was watching an anime, and I was confused about what was said versus the subtitles.

"こんな風に。。。少しずつ。。。他人になってよこんだね。"

So it was translated as:

"With the way things are going...just like this...we're slowly becoming strangers, aren't we?"

I'm not sure exactly what was said for the part that is highlighted in red. Is it a verb like "yokobu" or "yokomu" (neither of which I found in a dictionary so hence I don't think exist), or perhaps it's supposed to be the volitional form of 行く, so pronounced as "ikou/yukou"?

So what is the purpose of that word after なって and is it important to the meaning of the sentence? Can it be dropped or replaced?

Edit: Okay, I guess I was hearing it wrong. So they were saying:

他人になって行くんだね。"

So it's not volitional form. Never mind.

[undrentide]

"With the way things are going...just like this...we're slowly becoming strangers, aren't we?"

I'm not sure exactly what was said for the part that is highlighted in red. Is it a verb like "yokobu" or "yokomu" (neither of which I found in a dictionary so hence I don't think exist), or perhaps it's supposed to be the volitional form of 行く, so pronounced as "ikou/yukou"?

So what is the purpose of that word after なって and is it important to the meaning of the sentence? Can it be dropped or replaced?

Edit: Okay, I guess I was hearing it wrong. So they were saying:

他人になって行くんだね。"

なる : to become
〜て行く (te-form of verb + て＋行く） means it is on going.
So なって行く means the gradual change.
(And your interpretation of the sentence is correct.)