I'm sure it depends on how much the company values you, and how precarious your employment is, but assuming you are valuable to them at your current (well, previous) salary, you should be able to negotiate.

"You aren't paying me for where I live. It's actually quite irrelevant! You pay me for the value I generate. Continue paying me for the value I generate. Done!"

Of course, I've mostly worked for small companies that shit bricks when I leave. I imagine large companies have stupid cough, sorry... inflexible? policies in place that they can't find themselves troubled to work around.