Tbh she doesn't even deserve to "live on the streets" (obviously she could become a whore and live just fine) but I could also understand why Seiichi didn't abandon her, there are a plethora of reasons: maybe he has a big heart, he's forgiving, she's family, she's his literal mother, etc. but seems like none of it applies in this case.
Also stop reacting to my comments on this manga. I hate it!