The scenario you describe, where all the hydrogen in trillions of stars is consumed, is known as the "stellar era" or the "degenerate era" of the universe. It represents a very distant future, billions and billions of years from now.
During the stellar era, stars will exhaust their hydrogen fuel and transition to other elements through nuclear fusion processes. As stars run out of hydrogen, they will expand and become red giants or undergo supernova explosions, depending on their mass. Eventually, most of the remaining stars will become white dwarfs, which are dense, compact objects primarily composed of electron-degenerate matter.
As time progresses, the white dwarfs will lose their residual heat and cool down, becoming black dwarfs. These objects are no longer generating significant energy and will essentially become dark remnants. It's important to note that the timescales for these processes are extremely long, and we're talking about billions of years into the future.
During this era, the universe will become progressively darker and colder. Stellar activity will decline, and new star formation will become extremely rare due to the depletion of available gas and the vast distances between objects.
It's worth mentioning that our current understanding of the universe's ultimate fate and the specific details of the stellar era are based on theoretical models and extrapolations, as we cannot directly observe events that far in the future. Future discoveries and advancements in our understanding of physics may refine or change our understanding of these distant scenarios.