Sorry to hear about this trouble. There could be multiple reasons why application would crash. Could you please provide a few more details like:
Exact version of Illustrator
Does it gives any error code or message?
Where the files are saved (Network Drive/ System HDD/ Shared Folder on System /External HDD)?
When did this start happening? Are there any recent changes made to your system? For example, any antivirus, system updates or web extensions installed recently.
You may also try resetting Illustrator preferences. Preference settings are saved each time you quit the application. Crashing and unexpected behavior in application can be caused due to corrupt/ damaged preferences. Please follow these steps and let us know how it goes:
Close all Adobe applications.
Go to Location C:\Users\user\AppData\Roaming\Adobe
Rename Adobe Illustrator and Adobe Illustrator 24 Settings folders to Adobe Illustrator.old and Adobe Illustrator 24 Settings.old
Launch Illustrator from the Creative Cloud.
Please note that resetting preferences will remove all the custom settings and Illustrator will launch with default settings. This way all your old settings will be saved in .old folders and Illustrator will recreate new folders with default settings.