I read "Venom: Shiver", a 5 part miniseries that opens up the Venom solo comics.
It's definitely a thing. Literally, it's pretty much just The Thing with the Venom symbiote and Men In Black thrown in because, f**k it, they don't even know what they're doing anymore. I think this came out in, like, 2003 or 2004, and you can buy all 5 issues for, like $8 on the Marvel Digital Comic store. It's...alright. The art is kinda...weird. It's not exactly bad, but it isn't good either. I'd give it about a 5/10, maybe.
Also Eddie Brock isn't even mentioned, the suit is hostless here and jumps from body to body.