Is your basil wilty? It could be bacterial leaf spot.

You can transplant the healthy shoot. Make sure to keep it far away from the infected plant.

The leaves aren't wilting at all :/ They just look healthy and like they're growing and then the next day a third of it will be black and dying.

Hmmm. It can't be bacterial wilt. It might be bacterial leaf spot, but there are so many basil diseases.

Pictures are required if you wish to obtain an ID.

It's kind of hard to see because there aren't that many leaves left but the leaf on the left most branch is the only one that's been heavily affected right now. It grew a couple days ago and then the spot started and now most of the leaf is gone. The branch/stem in the bottom of the pic is the only one that looks healthy and it's the one I'm considering transplanting. The branch on the right constantly gets new leaves and sometimes they grow to how big they are right now but I saw (and I couldn't really get a picture of it) that the two tiny leaves that were coming in are already brown and dead. Next time I'll start the basil from seed -_-

What kind of basil is it?

This is the tag that it came from. Also today I noticed some yellow dust coating the soil in the center of the pot which is the one that the basil came with, which you can barely see here:

It looks like mildew or mold but I haven't watered the plant in almost a week!

It's probably powdery mildew. Test the soil. Is it wet or dry? Sorry with all the questions, but it's hard to identify. Does the pot have drainage holes? How much sun dies it get daily?

The soil is pretty dry and it has several drainage holes. It probably gets a few hours a day? I'd say around 5? And it's ok to ask questions! I want to know what it is although I'm pretty sure this plant is done for, at least I'll know for future reference

Does your basil leaves turn yellow then to black? Downy mildew makes your basil leaves turn yellow then to black. Before, have you watered the leaves, or just the ground?

I've been tried to only water the soil ever since the first day I moved the plant from the original nursery pot. There might have been some water splash but I haven't consciously watered the leaves, certainly not over the past week and a half. Also, the leaves don't really turn yellow. They are green then a brown spot appears, usually on the edge of the leaf, and then continues to darken and shrivel up until it dies.

Honestly I don't know what it is. I would transplant any healthy shoots/leaves to another pot. You could try spraying it with fungicide. Trim any infected leaves off, and if it's bone dry (the soil I mean) water it, careful not to get any water on the leaves. My guess is still mildew.

I transplanted one that looked ok today but I'm not holding my breath. I think the soil might have been infected when I brought it home because the container soil I used didn't have any of that yellow mildew on it. Thankfully it was only $5...

Ah, yes. The soil was most likely infected. Keep me updated on the healthy one!