The woman with Fox Quirk that he saved from an angry mob of civilians

Ever since Izuku had been discharged from the hospital, he found no opportunity or even have the courage to ask for such a thing from any women he saw and met. In the end, he decided to leave U.A since he believed he is a danger to everyone, believing that U.A and everyone who resided there will be in grave danger if All For One decided to launch an attack in an attempt to retake One For All.

So to not put anyone in danger, Izuku left U.A and even considering discard the idea of passing One For All on in the "natural way" as well.

Once learning that he is no longer at U.A, some of the pro-heroes left to search for him. Sometime later, his classmates also joined in the search as well. As this is going on, Izuku encountered a group of angry civilians.

After he saved her, she apologized for got him into her mess. However, he does not mind and even given her an umbrella. And after a conversation with her, he directed her to U.A so that she can find a shelter for herself.

For a moment, of course, Izuku did consider asking such a thing from her. However, he knows that it might be too much for her since she just got attacked earlier. So instead, he allowed her to leave for U.A instead.

However, their first meeting ended up not being their last one. After he defeated Lady Nagant, he was eventually found by all of his classmates, who proceeded to defeat him and take him back to U.A with them.

And upon seeing him collapsing after Ochaco is urging all refugees to let him in, she runs out with Kota to help him. As Izuku is losing his consciousness, he also made up his mind. This fox woman who saved him in return might have to do.