It depends on the implant.

Generally, they’ll be placed in a way that avoids interfering with nerves or blood supply. When it does happen, that’s a failure, not a normal part of the process.

Something like facial implants are usually solid (always, afaik, but I ain’t sith enough to deal in absolutes) rather than injected. You do have injections for cosmetics, but those tend to be into the lips almost exclusively.

The kind of injections that go into lips wouldn’t spill out after an injury. They use materials that aren’t liquid. Even the grotesque versions you see sometimes aren’t just bags of liquid under the skin.

Where you run into liquids, it’s going to be breasts and asses for the most part. The saline based ones will spill out if the “bag” they’re in ruptures. It’s just salty water, more or less, inside a sac.

Silicone implants are more of a gel, and thus wouldn’t “spill” in the same way, but if the container is ruptured can seep out into the body. It’s kinda like a thick jello in consistency, to use your own example.

But it is difficult to rupture the containers. They can be pierced, obviously, but enough force to just pop one is also enough force that you have other things to worry about.

Now, all of that assumes legal procedures. There are people out there that will essentially shoot caulk into their victims. And you’ll find some fucked up fakers that will do incorrect versions of otherwise safe-ish medical procedures, like transferring one’s fat from one place in the body to another.

And it’s important to note that there are procedures out there that do involve stuff that might match what you’re asking a bit closer, but they’re not exactly common