Well you said OneDrive 'web'. So it will not delete your files from you PC...
You may have a misconception about OneDrive app and OneDrive's web app. If you are backing up your files regularly and manually to onedrive.live.com , then the files are not actually 'synchronized' with your PC's files. The web application doesn't keep a look at your PC's files and doesn't add anything new or remove anything old from OneDrive when you do from your PC. It only does when you log on to onedrive.live.com and make any changes. Thus, this is an option if you manually upload files.
Whereas, the desktop and Store apps of OneDrive, may or may not keep a look at your files. For the desktop version, there is a dedicated OneDrive folder created on your PC where any changes (adding or removing) are always registered onto OneDrive. So that's not an option for 'backing up' your files because if they are only kept on OneDrive they will be lost when you lose them on your PC's drive too 'while having an active internet connection'.
Coming to the Store app of OneDrive, this gives you an option whether you want to manually upload your files and have no Saving folder on your PC, or edit your documents while always having the older copy backed up to OneDrive. Each time you hit save this copy gets uploaded to OneDrive without the fear of anything getting deleted. This can be achieved with the 'Offline' feature by OneDrive Store application. This is what you need.
Hope this helps. Comment if you need help. Best of Luck!
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