Dear all,
Thanks to Prof Baum, a new command is available on SSC. Its call "ghsurv".
This command implements the estimator proposed by Guell and Hu (2006), and aims to estimate duration type of models (like unemployment), when one only has information from repeated cross section data with incomplete spells.
For more details of the estimator and how it works see:

Original article
Güell, M. & Hu, L. 2006. Estimating the probability of leaving unemployment using uncompleted spells from
repeated cross-section data. Journal of Econometrics, 133(1), 307–341. doi:10.1016/j.jeconom.2005.03.017

and for a detail description:

Mundra, K & Rios-Avila, F. 2020. Using repeated cross-sectional data to examine the role of immigrant
birth-country networks on unemployment duration: an application of Guell and Hu (2006) approach. Empirical
Economics. https://doi.org/10.1007/s00181-020-01855-x

Best Regards,
Fernando