I'm most familiar with the term "softshell egg" for those.
Sometimes they have just a membrane on the outside.
Other times they are like the egg you found, with the membrane covered by a thin layer of the usual eggshell material. Normal eggs have a much thicker layer of that, which makes them strong and hard. When it is very thin it is weak, which is why that egg would crack or crumble as you handled it. The membrane is quite strong, which would be why it was difficult to actually open it.
That is what I would do, too.