I actually refused to send my current job a resume. The conversation went like this:
Can you send them a resume?
No- here's my LinkedIn.
But can you send them a resume?
OK, can you come in for an interview?
A month passes.
Can you come in for another interview?
That's a double-edged sword. On one hand I have to be pretty careful not to burn bridges or hop jobs, cause if I want to stay around here I'll run out of both quickly. On the other hand established developers around here all know each other, pretty much, so the network effect is very, very strong.
And that even means easy intros to people who work remotely for interesting companies elsewhere (which seems to be more and more a thing.) Just in the last month I've met people, through my local network, who work for places like Trello, Circle, etc.
The Circle guy in particular- well, he came up to introduce himself after a talk I gave, and some of what he's doing for Circle is very much up my alley, so if I wanted a different job or a remote job (I don't at the moment) I might hit him up.