Eeesh... Yes, fleas can live in rugs... And blankets, and pillows. If you have a bad flea infestation, you may need to bomb the house with a flea killer!
At the very least, the cat needs a flea dip and everything needs to be washed - some things need to be thrown away too. What joy....
Really and truly, shame on your sister for not taking care of her cat. It is terribly irresponsible of her not to be sure her cat is healthy and taken care of - and comfortable! (Can you imagine the discomfort of being infested with fleas?)
What a good sister and cat caretaker you are to try to help this animal. Please also check carefully for ticks as it seems she is doing nothing to prevent them either...
Why not give a vet a call and ask this question? I'm sure any one of them would be happy to have a conversation with you about cat care. Sounds like you need professional help here! (Maybe even call pest control to fumigate for you...)
This is a big job and I am sickened that anyone would be so irresponsible with an animal. It's totally unnecessary too - all that cat needs is some Frontline (though it is very expensive - as pet ownership tends to be.)
Please keep us posted about this poor helpless animal that is at the mercy of your sister!