What does Islam offer to protect a child of a haram relationship?

Islam is against zina and condemns it and has rulings on punishing people who commit it like the punishment by stoning for married adulterers (on which at least all earlier scholars sunni's shi'a and ibadi's seem to agree) and we accept the hadith of the Ghamidi woman (الغامدية) whom has committed adultery during the time of the Prophet() whom's punishment was delayed until she gave birth and breast fed her child etc. (see also in sunan abi Dawod , an-Nasa'i and sahih Muslim ). I've not come across so far to any hadith explaining or presenting the future life of an offspring of such a relationship no matter if the parents have been punished by lashes or stoning. Therefore I'd like to know what the Islamic shari'a offers to protect a child of a haram relationship, such as it won't be treated badly or pointed at as a child of zina (negative attribute) in the community? *It would be great if the possibilities of punishment of the parents were addressed (for example stoned, punished by lashes, both, one)...*