This paper introduces a novel approach to cure fraction modeling, also known as long-term survival modeling, by focusing on scenarios where a portion of observations is not susceptible to the event of interest. We propose a new defective distribution model based on the Beta distribution, specifically utilizing the defective Gompertz distribution as a foundation, while accounting for censored data and covariates. We demonstrate that the resulting Beta-Gompertz distribution also exhibits defective characteristics, making it particularly suitable for modeling data with cure fractions. To perform inference on the parameters, maximum likelihood estimation is employed, and its asymptotic properties are examined through simulation studies. The proposed methodology is illustrated using a real-world dataset related to the survival time of patients with triple-negative breast cancer from the A.C. Camargo Cancer Center Hospital, located in S & atilde;o Paulo, Brazil.