My opinion? Once you start talking trillions of years, any civilization is going to shake out into one of three categories.
1. EXTINCTION - Pretty simple: a plague, a supernova, warfare, mass suicide... something happens to wipe them out. If they're lucky, Type 1 civilizations leave behind some data recordings, mysterious devices, and pretty architecture for future spacefarers to gawp at/get killed by.
1B. STAGNATION - Think Doctor Who's Time Lords or Lovecraft's Elder Race. The species eventually hits a cultural and technological plateau and stays there, whether from societal strictures or simply hitting some sort of insurmountable obstacle to further advancement. Most traditionally, this ends up with a dwindling huddle of xenophobic douche-canoes who are convinced of their own superiority and have no qualms with slapping the shit out of "lesser beings". Alternatively, you end up with a bunch of ruthless bastards stealing resources and tech from nearby cultures in a desperate attempt to find their way around whatever roadblock has them stumped. In any case, stagnant civilizations are less than pleasant and basically stuck in a holding pattern until something brings it all tumbling down, at which point extinction ensues.
2. ASCENSION - Wizards/hyperspatial manipulation/psychics/whatever become so predominant within the species that they bust out of the universe as we currently understand it and become something beyond our comprehension. Whatever happens next, they're beyond petty concerns like "heat death" or "laws of physics" at that point, and have little if any resemblance to the beings they were before.
3. FUCKING UP ROYALLY - Sometimes, you go for option 2 and things go horribly wrong (or right). They're not dead and not really stagnant either, but the state they've gotten themselves into isn't exactly a preferable alternative, for themselves and/or everyone else. The best example I can think of is from a manga whose name escapes me at the moment: they turned themselves into immortal ghost-things, but then found out that after a few eons pass and your original star system goes kaput, all you've got left to do is float through the cosmos and steadily go insane. Whenever they found a planet with sapient life, they would hungrily insert themselves into members of that race. The hosts would become infused with the space ghosts' unspeakable misery and suicidal urges and off themselves, taking the space ghost to the grave along with them. A few people with just the right kind of psychological damage instead assimilated the space ghost essence into their own bodies and became able to access their extradimensional abilities, so the planet would then have to contend with a horde of superpowered nutjobs in the wake of a global mass suicide epidemic. Basically, bad times for everyone involved.
Trying to think in terms of billions or trillions of years is how you get Original Flavor Cosmic Horror - sapient life is, by and large, utterly boned in the long run, and the only hope humanity would have to survive is by scrapping 90% of the things that define us, so we wouldn't really
be humans anymore. Trying to plan on that time scale is pretty much a fool's errand for anything with an even vaguely human mentality.