This is the chandelier

Is the can attached to that box in the ceiling?

How heavy is the new 'chandelier'?

From your 3rd picture, the white wire at the top that enters the box is the power and contains the ground. The ground is attached to the box. The metal clad wire leaving the box goes to the 'can' where the light is housed. The ground is provided by the metal cladding.

Can you show a new picture of the new light?

What Steve said.

If that doesn't make sense, I suggest you call an electrician and have this done right.

In the electric box, the Romex needs to have a strain relief installed. As is, the wiring is subject to chafing and is also against code.

Mike is correct. It's not a matter of IF but when that wire will short to the box. I've seen it happen. Put the proper fitting on the box (they come either as metal or plastic).

As far as the conversion goes, what exactly are we talking about? Flush mount and chandelier aren't usually terms that go together.

If we're just talking about a simple pendant, there are converters that will screw in and cover replace the existing recessed trim and give you a down light...

The can is attached by 3 screws at the bottom where it meets parallel with the ceiling. The wires are attached to the box just as you stated weedmeister. The ground is on the housing of the can. The new chandelier is 3 pounds. It mounts flush to the ceiling.

I can use a pigtail to connect the wires to the new chandelier. There's a recessed lighting converter bracket with the same ideology I intend to use, not removing the recessed light casing.

OK, the term is "surface mount" not flush (and chandelier doesn't quite describe it either). The proper way would be to ditch the recessed cans and install a proper box. The problem would be that wiring junctions would need to remain accessible, and it's unclear if there is sufficient slack in the ILLEGAL WIRING that you have to do it right easily. I suggest you get a competent electrician (i..e, not the bozo who put in the recessed lights to begin with).

Unfortunately, the yo-yo who did that crummy can job didn't leave you many choices; I can't see a safe, code-compliant way to do what you're proposing.

You could move the light locations so the existing cables reach new proper junction boxes, and patch the old ceiling holes. Alternatively, you could rewire the entire installation.

It's so easy for electricians to take advantage of homeowners. As long as we turn on the switch and the lights work, we praise them, unknowingly of the crap they put together in the ceiling.

Thank you guys a lot!

It wasn't an electrician that installed those recessed lights. I'd say it's a handy man special.

I faced something similar putting in some track lights and finding a way to feed them. Fortunately for me, there was zero weight on the box since the track attached to the ceiling directly to the joists. But what might help here is that there are boxes available (plastic) for Old Work that attach to the drywall for support. If you have enough slack in the NM (Romex) cable, you can wire inside a new box as Ron said. If the wire is too short, there is a device out there that allows you to splice NM cable end to end without a box.

possible box

splice kit

You're welcome to those splicing kits. Maybe they're fine, but I don't trust 'em.

If the drywall is compromised so it won't support a old work box, you could also use a "fan box". This has extendable legs that reach out and bite into the adjacent joists rather than being supported by the ceiling drywall. You can put them in using a hole not larger than the box itself. I've used these a couple of times.