That's assuming the friend hadn't noticed I'm guessing. ;-)

I'd clean it up the best that I could and then just let the friend know and ask if there was anything else that could be done.

I'd also offer to pay for any expenses to have the rug cleaned or replaced. Within reason of course.

And if the friend didn't understand that pets sometimes have accidents then I would look for a different friend!

Apologize, apologize apologize and hope my pet is damn cute. lol (Though anyone who is willing to let a giant malamute into their home likely isn't to worrying about expensive rugs.)

I'd clean it up, apologize and offer to pay to clean or replace the rug no matter what it costs. There is no within reason here. If your animal destroys or damages someone elses property it's your responsibility to fix it by whatever cost necessary.

I also wouldn't consider someone being angry their property was destroyed by my animal as an unfriend like thing to do. If you know your animal has potty control issues it was unfriend like to bring the animal in, chances are your friend was trusting you knew your animal wouldn't potty in the house. If it isn't a normal issue with your pet you should include that in your apology. Ex/ "I am so sorry. *my pets name* normally never potties in the house. Perhaps there was an odd smell on the carpet. I'll clean it up and if need be pay to have it professionally cleaned or replaced."

It's certainly not something to go finding new friends over.

http://farm3.static.flickr.com/2015/1746143139_b1da8a152c.jpg

"Hey dude, you know how you're always saying sh** happens? Well it did. Right over there. I'm sorry, I tried to stop her but could not. I will pay for the cleaning or the replacement."

There's really nothing more you can do. Either your friend will get over it or he won't that part is up to him (her).

I'm pretty sure your friend knows you didn't wake up that morning and plan to have fido poo and pee all over the carpet.

Next time fido stays home.

OR, you could all play the stinky poo shoe game!!
http://www.youtube.com/watch?v=ZySKOdV1__0

I would tell my friend that my dog had an accident and I would replace it if it can't be cleaned.

Yes I would offer to replace the rug if my animal messed it up. I think that is the fair thing to do.