Suppose if you anchor text with one keyword (ex: Livington) and some one searches for longtrail/phrase keywords that include the single word "livington" (example: "where is livington"). Then can the search results show your website for "where is livington" in page one if your competitors have less backlinks, less SEO, missing keyword in some parts of the page (description, tittle, header, article ) but you do have it on all places. Meaning, can you still get extra traffic for longtrail/phrase keywords even if you used only one keyword for anchor text?
A backlink isn't keyword specific. You'll get a backlink for any keywords on the page (even "click here"), but an exact match anchor text link from a relevant page with a high PR would be best. Profile links for example would be a link, but it would carry less "weight".
It is highly possible but we never can say for sure what Google will do. A link in anchor text should ideally have your keywords in it but if the keyword just has one word then just give it a try and see how it works. Go for more than word keywords and use them in the anchor text. That would really help.