You should be able to turn the source code into jQuery object and use it like usual from there.
var requestedSource = request.source;
$(requestedSource).find('a.something').first().text();
This works for me in a very simple test on jsfiddle.
Note that you may have to play around with whatever $.find() returns if you have more than one anchor element with the class "something" (I just used $.first() to simplify my example). In that case, you can iterate through the results of $.find() like an array.
If that solution doesn't work, another (but worse) way you could do it would be to write the requested code to a hidden div, and then run $.find() from the div (though if the first solution doesn't work, there is likely something going wrong with request.source itself, so check its contents).
For example:
$('body').append('<div id="requestedSource" style="display: none;"></div>');
And then:
$("#requestedSource").append(request.source);
$("#requestedSource").find("a.something").first().text();
If you're repeating this request often, you can also empty the hidden div by calling $.empty() on it when you're done processing:
$("#requestedSource").empty();
For best performance, you would want to store everything in a variable and write once:
var hiddenRequestSource = '<div id="requestedSource" style="display: none;">';
hiddenRequestSource += request.source;
hiddenRequestSource += '</div>';
$('body').append(hiddenRequestSource);
var myResults = $("#requestedSource").find("a.something").first().text();
$("#requestedSource").empty();