Because, by definition, a Type IV civilization can harness extragalactic energy, they might manipulate some of the extra dimensions revealed by string theory and create a sphere in which dark energy reverses polarity, so that the cosmic expansion is reversed.
Because, by definition, a Type IV civilization can harness extragalactic energy, they might manipulate some of the extra dimensions revealed by string theory and create a sphere in which dark energy reverses polarity, so that the cosmic expansion is reversed. Outside the sphere, the universe might still be expanding exponentially. But inside the sphere, the galaxies evolve normally. In this way, a Type IV civilization could survive even if the universe is dying all around it.
In some sense, it would act like a Dyson sphere. But although the purposes of the Dyson sphere would be to trap sunlight inside, the purpose of this sphere would be to trap dark energy, so that the expansion could be contained.
The final possibility is to create a wormhole through space and time. If the universe is dying, then one option might be to leave it and enter another, younger one.

