In my mind, salmonella is not the issue here. I would be generally worried about who knows what growing in the crumb-and-egg mixture over the course of a week.
Whole eggs, uncooked and in the shell, take a surprisingly long time to expire (even longer if you have farm eggs that haven't had the cuticle washed off). But once you crack them open and mix them with other ingredients, you drastically increase their capacity to serve as a growth medium for microorganisms.
My advice to you is do not reuse such a mixture after the cooking session during which it was prepared. Is it going to hurt you to put it in the fridge overnight, and then use it to make some cutlets for breakfast the next day? I doubt it. But we're not talking about caviar and saffron here; bread crumbs are cheap, and a little egg and seasoning is easy to throw together next time you need it.
If you're concerned about convenience, season the bread crumbs and put them in a resealable bag. Store this bag in a cool place and take just as much of the bread crumb mixture as needed each time you want to make a breading. Use a new egg each time and throw away the excess.