Short answer. If an illegitimate child dies without any issue of their own, their father or mother inherits their entire estate. If both parents are living and filiation is duly proved as to both, they split the estate equally between them, share and share alike.
What the law says
If an illegitimate child should die without issue, either legitimate or illegitimate, his father or mother shall succeed to his entire estate; and if the child's filiation is duly proved as to both parents, who are both living, they shall inherit from him share and share alike.
Civil Code, Article 993 — Parents Succeed the Child. Read the full provision →
The parent inherits the whole estate
Article 993 addresses what happens when an illegitimate child dies with no issue of their own — no children or further descendants. In that case, the surviving parent, father or mother, succeeds to his entire estate. There is no legitimate child in this picture to divide the estate against; the whole of it passes to the parent, without competition from any other class of heir.
Both parents share equally if both survive
Where filiation is duly proved as to both parents and both are still living, Article 993 has them inherit share and share alike — an equal split between father and mother, rather than one excluding the other. The article does not give one parent priority over the other once both filiations are established, and it does not require the parents to have ever been married to each other.
Why the Family Code's legitime change does not alter this rule
The Family Code changed how much an illegitimate child inherits from a parent when a legitimate child is also an heir — halving the illegitimate child's legitime relative to a legitimate child's. That modification concerns the child's share of a parent's estate. It has no bearing here, because Article 993 addresses the reverse situation: a parent inheriting from the child, with no legitimate child in the picture to compare shares against.
What has changed: no more sub-classifications
One part of the later law does bear on this article. The Civil Code once split illegitimate children into different sub-classes with different succession rules; the Family Code abolished those distinctions and recognizes a single class of illegitimate child. So Article 993 should be read as applying uniformly to any illegitimate child, without regard to the old sub-classifications the original text was written around, and without treating any one sub-class more favorably than another.
If neither parent is left either
Article 993 only reaches as far as the parents. Where neither father nor mother survives to inherit, a different, following rule takes over: the surviving spouse of the illegitimate child succeeds to the entire estate, or, if brothers, sisters, nephews, or nieces of the deceased also survive, the spouse takes half and that group of relatives divides the other half. It is also worth remembering that an illegitimate child has no intestate right to inherit from the legitimate relatives of their father or mother, and the reverse is equally true — that exclusion runs both ways under the Code.