Yes, quite a lot of people. I've written a previous answer about what the Black Death was and how it killed people here, but it did not have a 100% mortality rate.

Bubonic Plague - where the bacteria infects the lymphatic system - has a highly variable mortality rate but on average it's only around 40% on its own. Pneumonic Plague, which occurs when the bacteria infects the respiratory system, has a 95% mortality rate and kills in about 48 hours. If someone got an infection in the lungs, they were pretty dead, but even then around 5% of people would have naturally recovered. Of victims lucky enough to avoid a lung infection, around 60% would have survived naturally.

It is theoretically possible to work out what percentage of people infected survived, but to do that accurately you would need to know the proportion of people with pneumonic plague, the proportion of people with bubonic plague, and the overlap. Unfortunately that data does not exist.