Drop box is not an effective way to share your file as you have discovered. It should be hosted from FileMaker Pro or FileMaker Server so that each user can use Open Remote from FileMaker Pro to open and access the database.
I share this individual's problem. Two of us use the database, one more often that the other who only enters data into one or two fields maybe three times a week. Other folks access the data via PDF or CSV files exported by scripts in the database when changes are made.
Most of the time the system serves us well but we have had a couple of times when conflicted files have been generated. The fellow forum member's request to mark a file as "In use" or alternatively blocking use of the file until it has been closed by the first user would be a great help.
Does anyone have a suggestion other than telling us that using DropBox is ineffective?