Let's say that there was a modern day "black death"; it kills one-third of the entire population of the world, 2.something billion people.

What would that end up doing in the short term? Long term?
Would our civilization be able to survive it?

Note that it would not be "one in every three people die evenly"; instead, some areas might see entire cities virtually wiped out, others might see little effect. But it would follow viral patterns, so that areas that have more travel etc. are more likely to be hit.
Also note that it would be like "2 billion people die in a week". It would follow a pattern of epidemic that would take about 2 years to run its course, the peak of its mortality rate happening at about the one-year mark, and then dropping slowly from there.

RPGPundit

Where would it start?

If it started in a major metropolitan area of a developed nation, that city would likely be placed under restrictions or perhaps outright quarrantine. If it started in an undeveloped nation, travel to and from that area would probably be restricted and later prohibited outright as the epidemic became evident.

Here is a story you might want to read.

Big questions:

At what point does local society collapse? What are the indirect consequences? (imagine if Pakistan's military decided to make a go for Kashmir if India was taking the worst of the plague) Is the plague treatable? Do you develop immunity?