is it possible to identify who has removed Usergroups from a Web?
If it is not possible, what is the best way to track the changes.
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If you have Site Collection Audit Logging enabled (Site Actions -> Site Settings -> Configure audit log settings,) which hopefully you do, you can view the Audit reports for the site. It will show the group deletion under "Security Settings"
Since you are using SharePoint foundation you might want to check it through this way,
Another option would be to check the IIS logs (configured in Central Admin -> Operations -> Usage Analysis Processing, will also tell you where they are stored if enabled).
some people face problems re-creating deleted groups so follow this post if you do,