His friends would probably take care of him. Midoriya would be very eager to help, using his kind-hearted nature. He would make sure Todoroki is fed and comfortable.
Todoroki's character development in time travel fanfictions can be quite profound. He may start as a somewhat aloof character, but through time travel, he begins to understand the importance of relationships more deeply. When he travels back and witnesses the relationships he could have had or lost, it makes him cherish the ones he has in his original timeline. His view of heroism also evolves. He realizes that being a hero isn't just about using his powers but also about making the right choices at the right time, which is especially highlighted when he has to make decisions that could change entire timelines.
One interesting 'Shoto Todoroki kidnapped' fanfiction could be where his friends from UA have to go on a rescue mission. They use their quirks in unique ways to track him down. For example, Deku might use his enhanced strength and ability to analyze the situation to find clues.
Todoroki was on a mission to rescue some hostages. As he entered the building, he didn't notice the hidden traps. One of the traps, a powerful blast of energy, hit him directly. He was thrown back, hitting his head on a wall. His vision blurred and he could feel a sharp pain in his ribs. He struggled to get up, but his body was in shock. The villains took advantage of his weakened state and closed in on him. He thought about his training and tried to gather his strength to fight back.
One common theme is family. Given Todoroki's complex family situation in the original story, many fanfics explore his relationship with his father, mother, and siblings further. Another theme is friendship. They often show how Todoroki forms deeper bonds with his classmates.