Is it normal for new Romex to be spliced directly into old cloth wiring like this?

That's what's known as a **flying splice**, and it’s a massive code violation and a serious fire hazard. Electrical code requires every single wire connection to be contained within a listed junction box that is accessible without cutting into the wall. Wrapping a bunch of electrical tape around a connection and burying it behind drywall is exactly how house fires start, especially when you're mixing modern NM-B with that old 1950s cloth-covered wire. The problem with that old cloth insulation is that it's likely rubber-based underneath, which turns to dust once it reaches a certain age. When you move those wires around or they heat up from a load, the insulation flakes off and leaves bare conductors exposed. If those wires aren't physically secured in a box with proper strain relief, a little bit of tension or vibration can cause the wire nuts to loosen. Once that happens, you get arcing, and since it’s sitting right against a wooden stud, it doesn't take much to ignite the framing. You absolutely cannot leave it as is. The right way to fix this is to pull those wires into a plastic or metal junction box. If there isn't enough slack in the old cloth wiring to reach a box, you might have to mount the box right there and then run a new length of Romex to where you actually want your outlet. Just make sure the cover of that box remains visible on the wall—you can't bury it under new drywall. Sometimes people do this to make a house look like it’s been updated during an inspection. They’ll run new yellow jacketed wire from the panel or to the outlets, but leave the old dangerous stuff in the middle of the walls. Since you've allready got the wall open, take the time to trace where those old wires are going. It’s better to deal with the headache of a few extra junction boxes now than to have the fire department visiting later.

Seen this nightmare in a dozen 1950s ranch homes. If that's 14/2 cloth wire, the second you move it, the insulation is going to turn into charcoal. Grab a Carlon B114R blue box and some Wago 221 lever-nuts. Those Wagos are a lifesaver for old tinned copper beacuse they don't twist the wire and snap the brittle strands like a standard Ideal 73B might. If you’re short on slack, you coud use a Tyco CPGI-1116415-1 splice kit since it’s UL listed for concealment, but I’d still prefer a real 4-square box with a blank faceplate. Don't cheap out on the Scotch Super 33+ tape if you're reinforcing those old ends.

Reminds me of the days when guys would just do a Western Union twist, slap some friction tape over it, and call it a day. If that old stuff has the silver-colored wire, don't mistake it for aluminum—it’s just tinned copper. But man, that rubber under the cloth gets so gummy it’ll stick to your fingers like tar. If you try to strip it back and it just crumbles, you’re better off chasing that line back to the last good box. Don't go trying to save two inches of wire and end up with a short.

If you're dealing with that crumbly cloth insulation, you shold realy grab a Tyco Electronics CPGI-208169-1 Romex Splice Kit. It’s one of the few ways to legally repair a buried splice without installing a permanent, visible access plate on your wall. Since you're allready behind the drywall, this kit is way better than trying to cram brittle wires into a standard box. I’ve used these for years on old fifties renovations where there's zero slack. Just make sure the connections are tight before you close it up.

Quick update — I went ahead and bought some Wago lever-nuts like one of you suggested. You weren't kidding about that cloth insulation being brittle; it practically disintegrated the moment I touched it. I ended up installing a proper junction box with an access plate to keep everythign up to code. I feel way better knowing that flying splice is gone.