SPCA question, what do they do if the dog isnt adopted? How long?

I'm going with someone to drop off their 6 year old lab mix at the SPCA. It really sucks! She lost her house because the bank wouldn't help refinance it so she's got an apartment lined up and no animals, barely room for three kids and little money. I was wondering if the dog isn't adopted, how long do they have? What do they do with the remains? Would I be able to get them an urn or something with the dogs name on it? How does this all work?