Applies for:- QXP 2018, QXP 2019.

If the QuarkXPress crashes or there is a power failure on the machine then it keeps the data that is saved on the mentioned time given in the preferences(You need to save the project at least once so that it can use the autosave). 

So, when you open the QuarkXPress again and try to open the same project that crashed, you will find an auto-saved project in the folder where you have saved the project with $ sign. However, you need open the .qxp file. When you will open the QXP file, the $ sign file will be automatically removed.

You can use the autosave feature by going to Edit>prefrences>Application>Open & save.