I said this the last time something similar came up, but I feel it's best to pretty much assume the Fixer was paid by the employer. Anything else is just trying to create yet another money sink to try and keep the PCs from really being able to make anything, in my opinion.
In the case where they forgot to get one or no one did because they thought one of the others would, there is not a problem in the world with just giving them a free Fixer contact (a decent one with at least Conn 4, Loy 3). Honestly, that should be a given anyway with how important that particular kind of contact is.
End of streak . . . . I don't agree.
I think you are, at that point, setting a precedence. You've just told your players that they don't need to ever purchase a fixer as a contact, because you're nice enough to give them one. It's a reward for stupidity.
However, if you have told them ahead of time that they will all start with a free fixer, who is techinically the one who brought them together, that is fine too.
Another reason this situation might come up, is if the players decide that the heat in their home town is too much and they need leave town and start up in another city. If this case occured, and it was their choice to do it, I see no reason for them to have to deal with the consequences.