When people say that there is no end to space (or that space is infinite) what they mean is is terms of distance. So if you kept travelling away from the earth in a spaceship you would never reach a place were the universe ended, you could just keep going. This doesn’t mean that things don’t change within space all the time. Seasons change, caterpillars turn into butterflies, and sometime stars die quietly or sometimes with an explosion.
after stars die, most of them just stay where they are. But, if the die close to a black hole, they might eventually get sucked in. Also stars that die in binary systems can slowly pull gas from their neighbor star until they become unstable and explode! This is how “Type 1A” supernovae happen.