Dealing with outdated Google links

[Tinafay]

I wanted to know about how Google manages to re-search for URLs which exist in the index. Does anyone have a clue about it? I am referring to the presence of an index with keywords used to locate non-existent links. How long do we need to wait before the link fades away? I have removed the description text and the cache from Google listing. For this, I used a URL removal tool. But the link is still present despite not being related to the search criteria. What do I need to do? Please let me know of any suggestions.