How do big companies stay afloat hiring whoever's left?

Think about it this way: your task is to have an inflow of X engineers / year. You can: a) pay recruiters to do whatever they do to bring you candidates that match a certain spec. b) build relationships with local campuses and recruit smart new grads, train them, and turn them into very capable engineers in a few years. c) host various tech events and do the "come work for us" speech every now and then. d) post a job on the jobs page.

In a long run (and they operate with this perspective in mind) you have way more control over your outcomes with options a-c. If you want more people on the output - you commit more money, effort, etc to each pipeline, and you will get your increased quantity. With the jobs page - all you can do is post and hope.

So it is no surprise to me that jobs pages get stale sometimes. Don't let that discourage you from applying to large companies. Instead, learn to play by their rules. Reach out to recruiters at those companies. Often those guys can be way more helpful than your friend engineer. Go to the talks they host, eat free pizza, socialize :)

That being said, there are some big companies out there that outsource their recruiting entirely, so it is really hard to find a recruiter that would help you. There are also big companies that don't host any talks or meetups. So if that's the case - don't waste your time and skip em - its their loss.

Cheers :)