Yes this is possible. I’ve not used it but CRIU seems to do this. Someone could easily write a little wrapper around it to make the job as easy as a double click.
Using this tool, you can freeze a running application (or part of it) and checkpoint it as a collection of files on disk. You can then use the files to restore the application and run it exactly as it was during the time of the freeze. With this feature, application live migration, snapshots, remote debugging, and many other things are possible.