When an electromagnetic (EM) wave travels through space and encounters no matter or any objects, it will continue to propagate indefinitely, theoretically. In the absence of any obstructions or interactions, EM waves do not experience significant dissipation or decay as they travel through the vacuum of space.
According to the laws of classical electromagnetism, as described by Maxwell's equations, EM waves consist of oscillating electric and magnetic fields that self-sustain as they propagate. These fields are self-perpetuating and do not require a medium to propagate through. Hence, in the absence of any obstacles, EM waves will keep moving at the speed of light.
In reality, space is not entirely empty but contains extremely low-density particles, such as gas molecules, dust particles, and photons. Even though these particles are sparse, they can still interact with and scatter EM waves to some extent. However, these interactions are typically negligible over vast distances in interstellar or intergalactic space, where matter is extremely sparse.
Therefore, unless an EM wave encounters a significant obstacle or is influenced by gravitational fields, it will continue to propagate through space indefinitely until it interacts with matter or other particles, gets absorbed by a medium, or is redirected by gravitational effects.