I have a similar story to the second one.
When I was single I was asked to tutor (for free) a boy who was written off as helpless. Since it required zero preparation- or so I thought- and my personal expenses at the time were $10 a week I agreed.
The neighbor making the request explained that the boy comes from an abusive home- he gave me the details but it’s not worth repeating- and has no trust in adults. Even though he has no potential I would still be doing him a favor by getting him away from his house for an hour a day and by being there as an adult who he could trust. He did have great Rabbeim but they didn’t have the ability to give him the personalized attention he needed.
His mother gave me a long list of learning disabilities he has which prohibit him from retaining anything he learns. His Rebbe explained that even though he doesn’t know a thing of what they learn the school doesn’t leave him back since it won’t help (and at least this way he gets to socialize with kids his age).
I was told not to request him to do anything or correct him when he is wrong since he will take them as personal attacks.
On the first day he asked if he could read the translation of the Gemora from the English. Little by little, as the trust built up, I was able to correct him when he had the wrong translation or p’shat. One day, after reading a whole omud perfectly he closed his Gemora. “What are you doing?” I asked. To my astonishment, he said the whole omud by heart, word for word.
His mother later told me that for the first time in years his Rebbe actually filled out his report card, and his grades were in the 90s!
Next his mother asked me if I know anyone in yeshiva who could help her son in math since he wanted to learn how to tell time (on an analog clock). I told her I’d be happy to help him. After teaching him fractions he taught himself everything else and caught up to his class.
As it turns out, he was actually a very intelligent boy who never had a chance given his surroundings. I continued to tutor him just to get him out of his house.
This went on for three years, form 6th grade to the end of 8th grade. In 8th grade he applied to a respected yeshiva and was accepted but unfortunately his father didn’t let him go. His mother and siblings moved out of the neighborhood shortly afterwards and I saw them once and only for a few seconds since. (They came back to visit and were stopped by a red light as I crossed. His mother rolled down the window to say “hi” and thanks for everything. He was in the passenger seat and looked confident, much better than the scared boy he used to be.)