Inheritance Rights – Spouse’s and Children’s Right to Inherit Heir’s Inheritance Rights. Heir’s Inheritance Rights – Inheritance rights encompass every imaginable sphere of family relationships. In any given situation, a spouse, child, family member, or friend, may feel that they have a right to a portion of the decedent’s estate. Inheritance law governs the rights of a decedent's survivors to inherit property. Depending on the type of inheritance law your state has, a surviving spouse may be able to claim an inheritance despite what you may have written into your will. This statutory right of a surviving spouse hinges on whether a state follows the community property or common law approach to spousal inheritance.