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.
Another interesting concept is a Todoroki family fanfic set in an alternate universe. In this universe, the family could be a normal, happy family from the start. There would be no hero - villain drama, and it could show their day - to - day life, like family dinners, outings, and how they deal with normal family issues.
One idea could be that all his friends at UA plan a surprise birthday party for him. They decorate the common room with his favorite colors, blue and red. Another plot could be Todoroki spending his birthday with his family, trying to reconcile with his father on this special day. Maybe he receives a heartfelt gift from his mother that has a deep emotional significance.
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.
Some Tumblr blogs are dedicated to sharing and recommending fanfics. You can search for tags like #Todoroki family fanfic on Tumblr. There might be some users who regularly post their favorite fanfics or even write their own short Todoroki family fanfic pieces on their blogs.