Presumably you are asking about engines that are used once a space vehicle has escaped the Earth's gravitational sphere of influence, or is close to that point. Rocket exhaust during launch becomes a part of the Earth's atmosphere. This continues to be the case beyond low Earth orbit.
The fate of a tiny particle in the solar system depends on the size of the particle. For molecule-sized particles, solar radiation pressure dominates over gravitational force toward the Sun. Extremely small particles (e.g., individual molecules of rocket exhaust) will spiral outward and eventually escape the solar system.
Suppose that by some chance, several billion molecules of rocket exhaust inelastically collide and bind with one another. The resulting picogram dust particle now has a different fate than the fate of individual molecules (or even a dust particle comprising only millions of molecules). At this size, Poynting-Robertson drag becomes dominant and makes the dust particle spiral inwards toward the Sun.
Our Sun ignited about 4.6 billion years ago. Once a protostar ignites, the combination of stellar radiation pressure, stellar wind, and Poynting-Robertson drag clears out the gas and dust in a protoplanetary disk that didn't combine to form protoplanets in ten million years or so.