So let's say, a blog put a link to my website on the sidebar, resulting in many thousands of backlinks (since the blog itself has thousands of pages). Because of the success of this link, let's say my website goes significantly up in SERP. If that blog removes my link, will the search engines erase all the backlinks that the site had pointed towards my site, and thus put my SERP back to where it was before ?
Google or any other search engines take time in both recognizing backlinks and recognizing its absence. Suppose you put up your link on thousand on pages. It took 1-2 weeks in finding those links and Page rank juice starts flowing to your blog ... your blog will get up in serp ... but if you will remove those links it will not suddenly goes down. No one is extracting page rank juice from you. Its just that the juice you got till now is not available now .... The only problem being that it may sometime become suspicious to search engines. They may think sudden link surge and downs as paid link exchange program. so be careful.
1) A website may link to your site from thousands of pages but the searchbot will consider it as one backlink. Sorry to shatter your dreams of 1000 backlinks dear. 2) lets consider that your website goes significantly up in SERP & If that blog removes your link. The search engines will still consider it a backlink to your site TILL the backlink giving site gets indexed. 3) A SERP is affected by more than a single backlink. However, if 1000 backlinks do get cut off at the same time, your PR might go down and somewhere it will affect your ranking. But, If you have a few backlinks from very high PR sites & a good traffic to go with, your site might not be affected that much.