I deleted part of a form I was completing
It is hard to answer without knowing which operating system you use and which program you were using to fill out the form. In general, if the file isn’t in your Trashcan where other deleted things often go, it might be found among the temporary files (.tmp) stored by various programs. It also might aid your search if you start to fill out the form again just to see what your computer calls the form as a file, in order to get an idea of what to look for in the Trashcan or with temp files.
In general, unless you use backup copies, you should not expect software to think it’s smarter than you: when you tell the software to erase something, it should erase that, and not keep that. So, while there’s a chance to successful use of different unerase applications, it’s only a matter of luck.
LibreOffice does include a setting to store the version before-the-last-save as a backup copy (only one version is kept in a .bak file; see Options-Load/Save-General-Always create backup copy).