How do I recover Quicken files deleted by Force Quit on iMac?

Very simple, restore from your Time Machine backup. If you are not backing up your computer then that is a HUGE mistake and guarantees you will continue to lose data. To use Time Machine you only need to buy an external HD as Time Machine is pre-installed on your computer already. A External Hard Disk many users like is the OWC Mercury Elite Pro due to its pricing, high quality and reliability.

If you are not familiar with Time Machine please click Back up your Mac with Time Machine.

Are you saying that you no longer have a Quicken app on your Mac? I've never heard of force quit deleting an app. Have you checked the Applications folder?

For as long as I can remember with Quicken, it has always made an automatic backup of data every time it closes, unless that option is turned off in Quicken Preferences. If you have a Quicken app of any age, you should be able to restore from the backup by using the File menu > Restore from Backup. You may also be able to go to the Backup location (as show in Quicken Preferences) and double-click a file to open it.

Is that how you tried to restore? I don't know why a current version would be needed but anything's possible.

You may also want to try the Quicken support forum (and let them know up front what version of Quicken you have, if possible). https://community.quicken.com/categories/quicken-for-mac

Force Quit will "delete" files, or current work, only if they were never saved. When invoked, Force Quit does not touch an existing file.

The following from Quicken support may help: https://www.quicken.com/support/mac/how-backup-or-restore-your-quicken-data

Well, you should be making back-ups of all of your data on a daily basis, using Time Machine or some other backup/cloning application. Your most recent Quicken data file would be in that backup. If your Quicken app was damaged you could reinstall it from your original install disc or from your most recent backup too.

If you do not have such a backup strategy then you are simply out of luck and your data is gone forever. If your financial and personal data is important to you then it is important that you are prepared for catastrophes like this.