I used to own an 8-track player and some tapes. I never had that happen, but I imagine that for a while, the tape would just keep playing, slowing down as it did. If you let it go long enough, I imagine it'd start to sound like a broken cassette, where the speed becomes unstable and it really starts slowing down a lot, then eventually just stops. Of course, pulling the cartridge out would reveal a huge wad of tape in the player. I had one tape break at the splice, but fortunately for me, it broke in such a way that the beginning of the tape loop hadn't reached the part of the machine that pulls it in, so the tape just stopped playing, although the motor kept running. At that point, there was no way to fix it without opening the cart, since one of the loop ends was inside.

I remember reading an article that went into a lot of detail about how to open up videotapes and fix parts of them that were damaged. It used to be on obseleteskills.com, back when that site existed.
I don't know how similar that process would be with an 8 track, but I imagine it would be. The materials used for the tape would be pretty much the same.
I've never actually seen an 8 track player, either, but I love retro things, particularly outdated music technologies. I'd like to see one at some point. That, and a reel-to-reel tape player, which I've heard are a royal pain in the ass, but I'd still like to know what it looked like.

Oh, that is so cool. Was it one of the gramophones that you wind up, or was it electric?
I agree about turntables. The sound of vinyl is just so much nicer than mp3's. My family still owns a bunch of VHS tapes, but we don't have a working VCR, so unfortunately they're just gathering dust at the moment.

I have a pretty decent collection of vinyl myself. Most of it has been passed down from my parents, who weren't using it anymore anyway, so I've cleaned it up as best I can, and still very much enjoy listening to it.
The only reason I haven't bought any lately is because I don't have the space for it, sadly.
I was a 90's kid, so I should have loved CD's. But I really didn't, not even then when they were "in." They were much too easy to break, scratch, and mishandle for my liking. Not that I took especially good care of them when I was a kid, but still. It's no wonder they've been phased out, for the most part. I can't remember the last time somebody told me they were going out to buy music on a CD. Now, it's all about services like ITunes, Amazon, Bandcamp, Spodify, and so on. Not that I mind that, in itself. I have a pretty sizable digital collection of music, nearly 4 terrabytes, in fact. But I wouldn't give up my vinyl for anything. I think both digital and analog music has its place.