A Poisson model for survival could make sense in a setting where data is aggregated, e.g., you don't have data at the individual level, but instead have a count of the number of events (e.g. deaths) for a group of subjects, or a sum of the number of events in a single subject. As it is a parameterization (closely connected to the exponential distribution for survival times) it makes more assumptions than other semi-parametric approaches (e.g. Cox's model).

Many thanks for your responses. Will try it out this.