Rossby Wave packets (RWPs) are atmospheric perturbations located at upper levels in mid-latitudes which, in certain cases, terminate in Rossby Wave Breaking (RWB) events. When sufficiently persistent and spatially extended, these RWB events are synoptically identical to atmospheric blockings, which are linked to heatwaves and droughts. Thus, studying RWB events after RWPs propagation and their link with blocking is key to enhance extreme weather events detection 10-30 days in advance. Hence, here we assess (i) the occurrence of RWB events after the propagation of RWPs, (ii) whether long-lived RWPs (RWPs with a lifespan above 8 days, or LLRWPs) are linked to large-scale RWB events that could form a blocking event, and (iii) the proportion of blocking situations that occur near RWB events. To do so, we applied a tracking algorithm to detect RWPs in the Southern Hemisphere during summertime between 1979-2020, developed a wave breaking algorithm to identify RWB events, and searched for blocking events with different intensities. Results show that LLRWPs and the other RWPs displayed large-scale RWB events around 40% of the time, and most RWB events in both distributions last around 1-2 days, which is not long enough to identify them as blocking situations. Nearly 17% of blockings have a RWB event nearby, but barely 5% of blockings are linked to RWPs, suggesting that propagating RWPs are not strongly linked to blocking development. Lastly, large-scale RWB events associated with RWPs that lasted less than 8 days are influenced by the Southern Annular Mode and El Niño-Southern Oscillation.