In cases where a beneficiary cannot accept their share of the estate under the Intestate Succession Act, they can renounce or disclaim their entitlement. Renouncing or disclaiming means voluntarily giving up their rights to the inheritance. This decision could arise from various reasons, such as personal circumstances, financial considerations, or personal choice. When a beneficiary renounces their share, it is typically redistributed among the remaining entitled beneficiaries according to the act's provisions. Renunciation or disclaimer of inheritance rights usually requires a formal legal process and should be done following applicable laws and procedures.