The photos on one of my Facebook accounts seem to have lost a significant amount of resolution after they had already been posted. This account has other issues, for example, my timeline review is turned off but I am still asked to review anytime someone tries to tag me in something. I used to think online photos can't change, but I read somewhere that it is possible if the host website decides to rewrite them. Is there anything I could do to prevent this from happening?
one of my Facebook accounts seem to have lost a significant amount of resolution
Facebook (and other social media sites) compress photos while storing/displaying. Considering the amount of data that gets uploaded in these sites, its difficult to argue against it. This link talks about how you can minimize that to a small extent (but that article is old and not sure if those settings are still present). Brief googling brings up this guide from facebook.
I read somewhere that it is possible if the host website decides to rewrite them
That would depend on the usage agreement/terms and conditions that you agree to while signing up. As per Remco's answer users grant usage and modify right to Facebook.
If preserving the original quality (and metadata) is your requirement, you can look into dedicated photo storing websites like 500px, flickr and others. Google photos lets you choose the quality of uploaded images and offers unlimited storage on compressed images. However their compression algorithm IMHO is better than that of facebook and the loss of quality is negligible.
Short answer: no. Especially not in the case of facebook, where you explicitely give them the right to use your images almost as they want. From their terms:
Specifically, when you share, post, or upload content that is covered by intellectual property rights (like photos or videos) on or in connection with our Products, you grant us a non-exclusive, transferable, sub-licensable, royalty-free, and worldwide license to host, use, distribute, modify, run, copy, publicly perform or display, translate, and create derivative works of your content (consistent with your privacy and application settings).
Note the modify and publicly display parts of that. As a side note: you also give them the right to transfer or sublicense your images...
And those terms do not prevent them modifying images marked as private.
The photos on one of my Facebook accounts seem to have lost a significant amount of resolution after they had already been posted.
This is not damage, this is facebook deciding to not store the original resolution but work with a reduced resolution. They also strip most metadata.
They are NOT A BACKUP SITE FOR YOUR PHOTOS.
I used to think online photos can't change,
You upload a photo to someone else computer. What train of thought can you logically come up with that makes it impossible for the owners of said computer to not be ABLE to change this photo?
Is there anything I could do to prevent this from happening?
Do not upload your photos to a place you do not control.