We have a general rule about life: anything that eats must also shit. As this entity wanders the galaxy in search of our sun it will leave a trail for us to follow. We will be able to track the brownian motion of this trail with our new b-ray telescopes. Our best defence may be to ship all of our stored airborn pollutants to a point between the entity and our star. The sun will appear so dim that the entity will choose another victim.
We already know of such a star eating phenomenon: black holes. We shouldn't jump to the conclusion that they are alive, much less intelligent, but hey nobody messes with them so they must be pretty smart. Fortunately they don't seem to be too mobile so they won't come to us. But they might expand and suck us in...
A mini hole, smaller than a donut hole, with the mass of a Wolf-Rayet star that mercilessly sucks in anything in its path as it dances around the universe. So small as to be invisible to our instruments, so massive that it warps space time making it even harder to detect. Intelligence? It's just a mindless bully bent on destruction. No smarter than that punk kid dealing drugs on your corner.
We know that virii can survive extreme heat, cold and even outer space. Even the corrupt environment of your body can host one or more virii. Who's to say the sun is immune? A cozy warm environment with no discernible bacterial competition and a virus could have its way with our sweet sun.