What inheritance includes

Article 776. The inheritance includes all the property, rights and obligations of a person which are not extinguished by his death.

Article 781. The inheritance of a person includes not only the property and the transmissible rights and obligations existing at the time of his death, but also those which have accrued thereto since the opening of the succession. (Civil Code of the Philippines)

If rights and obligations are extinguishable by death, they cannot form part of the decedent's inheritance. In other words, such rights and obligations cannot be transmitted via succession.

Article 781 speaks of the general rule in property law that accessions, accessories and fruits follow the property to which they attach. Hence, even if civil fruits become due and demandable after the death of the decedent, they form part of the inheritance because, for example, the building out of which such fruits arise is also a part of the inheritance.