In this N4 lesson, there is this sentence:
独立して暮らせるように働き始めた。
My question is not about ように, but about everything that precedes it. AFAIK:
I am struggling to put these two pieces together to mean what they’re supposed to, when linked with て. Is there a Bunpro lesson that covers this usage of て?
It’s covered in Lesson 5 of N5.
I presume you’re referring to this one? That’s the only て point I can find in that lesson. And I don’t think it’s the right one for this phrase.
The phrase is not:
“To be independent and then to be able to live”… i.e. two verbs linked with “and then”.
Rather it is:
“To be able to live independently”. It’s almost like the part preceding the て is being used adverbially. That’s very different from the lesson I linked above.
i believe this kind of verb-verb construction can be conceived of as “to be independent and live” but we wouldn’t say that in English so it becomes “to live independently”
the linked grammar point offers both explanations for “and” and “then” so I think it does cover it, but for some reason the example sentences only include “then”
but another example would be like 持ってくる which you can translate as literally hold and come (i.e. bring)
The “and then” translation applies to chronological lists of activities. That doesn’t really apply here. These are more just descriptive items than activities that occur in sequence.
Otherwise, it’s more of an “and” translation. So something like “to be independent and live.”
That’s not terribly natural English, but such is the nature of translation.
Going of what some others have already brought up, the explanation that is the closest to what you’re probably looking for is an N4 lesson.
In your sentence, the verb 独立して is acting as a means or circumstance in which one can live, so it’s modifying 暮らせる in this way and thus in translation it becomes “to be able to live independently”. While the lesson doesn’t explicitly state that this construction can be used adverbially, you can see it acting this way in one of the example sentences.
寝坊をしたので慌てて準備をした。
Since I overslept, I got ready in a flurry.
Here, 慌てて is being used to describe 準備する in the same way, and is also translated as such, with “in a flurry” describing “got ready”. Idk if I put that in a way that makes sense but hopefully it helps clear things up
You know, I think that is it. And you want to hear something funny? I’ve been in like 1 hour of conversation with 3 different LLMs about this topic before posting here. And the very first link that ChatGPT gave me an hour ago was… that link. But I argued back with it at the time, and then went through a million other bad answers before coming here.
My bad argument at the time was that the lesson says:
the nuance is quite often that ‘(A) allowed/led to (B)’
And I argued that “being independent does not allow living”. But when I think now instead of “by means of” or a tool… then it’s easy to think of “being independent” as a tool that one lives by the means of. And it also fits nicely with my belief that this is an adverbial usage, which I still believe despite it not being called out anywhere explicitly.
These things are much harder to visualize when it’s a stative verb. Compare “living by means of being independent” vs “traveling by means of riding a bike”. The former is so much more abstract. I think I’m also realizing that maybe I’ve always viewed “living” as a binary, passive thing (alive or not), whereas this concept treats it more as an active continuous state.
ありがとう ! 
And you want to hear something funny? I’ve been in like 1 hour of conversation with 3 different LLMs about this topic before posting here. And the very first link that ChatGPT gave me an hour ago was… that link.
I don’t blame you for not trusting ChatGPT lol, I also would have been skeptical.
Also, you’re welcome! Good luck on your studies :))