Can An Illegitimate Child Inherit Wealth From His/Her Biological Mother?

There are some Hadiths that state that an illegitimate child cannot inherit the wealth of his biological father (See Sunan Ibn Majah 2745 and Jami` at-Tirmidhi, Vol. 4, Book 3, Hadith 2113). However, I have read somewhere that an illegitimate child can inherit the wealth of his biological mother. I would like to know what is the basis of this claim? Is there any evidence from the hadith scriptures that suggests that an illegitimate child can inherit wealth of his biological mother? What if such a child is poor and there is no one there to look after him after his or her parents have given birth to hom/her and left such a child without any support?