I have encountered numerous fake profiles that have survived for months/years. Many of these represent businesses that should really be pages. Others are accounts that are used on hate groups/pages exclusively and have highly offensive fake names.
The worst example I've seen was a vicious cyberbullying profile that Facebook allowed to accumulate hundreds of friends, under an obviously fake name, despite a large number of abuse reports.
There are a number of accounts we created for inanimate objects while at uni which are still around. They all have a certain amount of friends and photos though.
We also used to create fake people using photos from stock art libraries and try to create realistic social lives for them, with our aim being that our real friends would eventually start enquiring after the fake people as if they knew them.
Fake accounts get shut down very quickly, they have a mechanism that seems to detect those accounts very quickly.