At a surface level: No. If you're imagining, say, a firework and the trail it leaves, with "sun-stuff" behind it - there's nothing like that. This has been covered in detail by other posts.

At a more detailed level: Yes-ish. The Sun is constantly emitting particles - not just massless light but also massive particles, the "solar wind". As the Sun (and the entire solar system) move through space, this creates a "wake" or elongated "bubble" called the heliosphere. Notably, this is much larger than just the Sun - all the solar system's planets are well inside the heliosphere. This diagram demonstrates the effect.

The heliosphere is invisible and undetectable to the naked eye or any "human-level" interaction; you need special equipment to detect the differences between it and the surrounding interstellar medium. From a human perspective they would both "feel" just like empty space.