In Burning Wheel (both Gold and Revised), players can (and are strongly encouraged to) start with a close connection to one or more NPCs, in the form of the relationship mechanic.
Now, it's pretty clear from the text relationship NPCs are meant to be easily accessible:
During play, [relationships] are used by the players and GM to get into and out of trouble, provide detail and depth to the background, and create conflicts...
Meeting and consulting with a relationship character doesn't require a test. By spending resource points on establishing relationships with these characters, it is assumed that all the details of contact and communication are worked out ahead of time. So long as it is reasonable feasible in the game context, a player can have his character visit his relationship contacts freely and often.
But this is all about not having to make tests (in the style of Circles) to go to seek your relationship characters. What about the opposite way? Do players have the ability to have their relationship characters come to them?
Here are hypothetical examples where the distinction in the question actually makes a difference:
My character falls in battle. Can I use my relationship to narrate that my lover comes to scoop me up from among the dead and dying?
My character's in jail and not going anywhere. I look at my character sheet and notice my nasty uncle (minor hateful family) hasn't shown up for a few session. My character would never reach out to that jerk for anything; also he doesn't really have the means to, right now. But I as a player think it would be great fun to bring him in. Can I introduce my uncle into the storyline, come to buy me out of jail (and straight into indentured servitude, working for that conniving toad! oh no!)?